Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
195 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5426 | C2 | 1 | 2 | yes | maximal |
| 3 | #5389 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #3080 | — | 3 | 1 | no | maximal, Sylow |
| 5 | C2×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 6 | #870 | — | 4 | 1 | no | maximal |
| 7 | C4×SL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 8 | #859 | C22 | 1 | 4 | yes | — |
| 9 | C2×#125 | — | 3 | 1 | no | — |
| 10 | C4×#41 | D3 | 1 | 1 | yes | characteristic |
| 11 | #479 | — | 3 | 4 | no | — |
| 12 | #478 | — | 3 | 4 | no | — |
| 13 | #428 | — | 3 | 2 | no | — |
| 14 | #423 | — | 3 | 1 | no | — |
| 15 | #417 | — | 3 | 2 | no | — |
| 16 | #41⋊C3 | Q8 | 1 | 2 | yes | — |
| 17 | C2×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 18 | C3×C42 | — | 4 | 1 | no | — |
| 19 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 20 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 21 | C2×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 22 | C2×M16 | — | 3 | 2 | no | — |
| 23 | #125 | — | 3 | 4 | no | — |
| 24 | #125 | — | 6 | 1 | no | — |
| 25 | #125 | — | 6 | 1 | no | — |
| 26 | C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 27 | C4×D4 | — | 3 | 2 | no | — |
| 28 | #117 | — | 3 | 1 | no | — |
| 29 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 30 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 31 | C2×C42 | — | 3 | 1 | no | — |
| 32 | #107 | — | 3 | 4 | no | — |
| 33 | #106 | — | 3 | 4 | no | — |
| 34 | C4⋊C8 | — | 3 | 4 | no | — |
| 35 | #103 | — | 3 | 4 | no | — |
| 36 | #102 | — | 3 | 4 | no | — |
| 37 | C2×C3×C4 | — | 4 | 1 | no | — |
| 38 | C2×C3×C4 | — | 4 | 2 | no | — |
| 39 | C2×Dic3 | — | 4 | 4 | no | — |
| 40 | SL(2,𝔽3) | C2×Q8 | 1 | 1 | yes | characteristic |
| 41 | #41 | — | 3 | 2 | no | — |
| 42 | #41 | Dic6 | 1 | 2 | yes | — |
| 43 | C2×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 44 | C2×D4 | — | 3 | 1 | no | — |
| 45 | C22×C4 | — | 3 | 1 | no | — |
| 46 | C22×C4 | — | 3 | 2 | no | — |
| 47 | C22×C4 | — | 6 | 2 | no | — |
| 48 | M16 | — | 6 | 4 | no | — |
| 49 | C2×C8 | — | 3 | 4 | no | — |
| 50 | C4⋊C4 | — | 3 | 2 | no | — |
| 51 | C4⋊C4 | — | 3 | 4 | no | — |
| 52 | C4⋊C4 | — | 6 | 4 | no | — |
| 53 | C4⋊C4 | — | 6 | 2 | no | — |
| 54 | C4⋊C4 | — | 6 | 4 | no | — |
| 55 | C22⋊C4 | — | 6 | 1 | no | — |
| 56 | C42 | — | 3 | 2 | no | — |
| 57 | C42 | — | 3 | 1 | no | — |
| 58 | C42 | S4 | 1 | 1 | yes | characteristic |
| 59 | C22×C3 | — | 4 | 1 | no | — |
| 60 | C3×C4 | — | 4 | 2 | no | — |
| 61 | C3×C4 | — | 8 | 2 | no | — |
| 62 | Dic3 | — | 8 | 4 | no | — |
| 63 | C23 | — | 3 | 1 | no | — |
| 64 | Q8 | — | 3 | 1 | no | — |
| 65 | Q8 | C2×Dic6 | 1 | 1 | yes | characteristic |
| 66 | D4 | — | 3 | 2 | no | — |
| 67 | D4 | — | 6 | 1 | no | — |
| 68 | C2×C4 | — | 3 | 1 | no | — |
| 69 | C2×C4 | — | 3 | 2 | no | — |
| 70 | C2×C4 | — | 3 | 2 | no | — |
| 71 | C2×C4 | — | 3 | 2 | no | — |
| 72 | C2×C4 | — | 6 | 4 | no | — |
| 73 | C2×C4 | — | 12 | 2 | no | — |
| 74 | C2×C4 | — | 12 | 4 | no | — |
| 75 | C2×C4 | C2×S4 | 1 | 2 | yes | — |
| 76 | C2×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 77 | C8 | — | 6 | 4 | no | — |
| 78 | C2×C3 | — | 4 | 1 | no | — |
| 79 | C2×C3 | — | 4 | 2 | no | — |
| 80 | C22 | — | 3 | 2 | no | — |
| 81 | C22 | — | 6 | 2 | no | — |
| 82 | C22 | C22×S4 | 1 | 1 | yes | characteristic |
| 83 | C4 | — | 2 | 2 | no | — |
| 84 | C4 | — | 3 | 1 | no | — |
| 85 | C4 | — | 3 | 1 | no | — |
| 86 | C4 | — | 6 | 2 | no | — |
| 87 | C4 | — | 12 | 4 | no | — |
| 88 | C4 | A4⋊Q8 | 1 | 2 | yes | — |
| 89 | C3 | — | 4 | 1 | no | Sylow |
| 90 | C2 | — | 6 | 2 | no | — |
| 91 | C2 | C2×A4⋊Q8 | 1 | 1 | yes | characteristic |
| 92 | C2 | #5923 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #5389 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41⋊C3 | 2 |
| #5426 | 2 |
| #5389 | 2 |
| #3080 | 3 |
| #870 | 4 |