Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
92 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #4628 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #2195 | — | 3 | 1 | no | maximal, Sylow |
| 5 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 6 | #984 | — | 2 | 1 | no | — |
| 7 | #131⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | #827 | — | 4 | 1 | no | maximal |
| 9 | #578 | D3 | 1 | 1 | yes | characteristic |
| 10 | #510 | — | 3 | 1 | no | — |
| 11 | C2×Q32 | — | 3 | 1 | no | — |
| 12 | #473 | — | 3 | 1 | no | — |
| 13 | #362 | — | 3 | 1 | no | — |
| 14 | #359 | — | 3 | 1 | no | — |
| 15 | #350 | — | 3 | 1 | no | — |
| 16 | #41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 18 | #226 | — | 4 | 1 | no | — |
| 19 | C3×D8 | — | 4 | 1 | no | — |
| 20 | Dic12 | — | 4 | 1 | no | — |
| 21 | C3⋊C16 | — | 4 | 1 | no | — |
| 22 | 2−1+4 | — | 2 | 1 | no | — |
| 23 | #137 | — | 6 | 1 | no | — |
| 24 | #137 | — | 6 | 1 | no | — |
| 25 | #135 | — | 3 | 1 | no | — |
| 26 | C2×Q16 | — | 3 | 1 | no | — |
| 27 | C2×Q16 | — | 3 | 1 | no | — |
| 28 | #131 | C2×D3 | 1 | 1 | yes | characteristic |
| 29 | Q32 | — | 6 | 2 | no | — |
| 30 | Q32 | — | 6 | 1 | no | — |
| 31 | SD32 | — | 6 | 1 | no | — |
| 32 | M32 | — | 3 | 1 | no | — |
| 33 | C2×C16 | — | 3 | 1 | no | — |
| 34 | #108 | — | 3 | 1 | no | — |
| 35 | #101 | — | 6 | 1 | no | — |
| 36 | C3×D4 | — | 8 | 1 | no | — |
| 37 | Dic6 | — | 8 | 1 | no | — |
| 38 | SL(2,𝔽3) | D8 | 1 | 1 | yes | characteristic |
| 39 | C3×C8 | — | 4 | 1 | no | — |
| 40 | #41 | — | 6 | 1 | no | — |
| 41 | #41 | — | 12 | 1 | no | — |
| 42 | #41 | #67 | 1 | 1 | yes | characteristic |
| 43 | C2×Q8 | — | 4 | 1 | no | — |
| 44 | C2×Q8 | — | 6 | 1 | no | — |
| 45 | C2×Q8 | — | 6 | 1 | no | — |
| 46 | Q16 | — | 3 | 2 | no | — |
| 47 | Q16 | — | 3 | 1 | no | — |
| 48 | Q16 | — | 6 | 1 | no | — |
| 49 | Q16 | — | 6 | 1 | no | — |
| 50 | Q16 | — | 12 | 1 | no | — |
| 51 | SD16 | — | 6 | 1 | no | — |
| 52 | SD16 | — | 12 | 1 | no | — |
| 53 | D8 | S4 | 1 | 1 | yes | characteristic |
| 54 | M16 | — | 3 | 1 | no | — |
| 55 | M16 | — | 6 | 1 | no | — |
| 56 | C2×C8 | — | 3 | 1 | no | — |
| 57 | C16 | — | 6 | 1 | no | — |
| 58 | C16 | — | 6 | 1 | no | — |
| 59 | C22×C3 | — | 16 | 1 | no | — |
| 60 | C3×C4 | — | 4 | 1 | no | — |
| 61 | Dic3 | — | 16 | 1 | no | — |
| 62 | Q8 | — | 6 | 1 | no | — |
| 63 | Q8 | — | 12 | 1 | no | — |
| 64 | Q8 | — | 12 | 1 | no | — |
| 65 | Q8 | — | 12 | 1 | no | — |
| 66 | Q8 | #213 | 1 | 1 | yes | characteristic |
| 67 | D4 | — | 2 | 1 | no | — |
| 68 | D4 | — | 3 | 1 | no | — |
| 69 | D4 | — | 12 | 1 | no | — |
| 70 | C2×C4 | — | 3 | 1 | no | — |
| 71 | C2×C4 | — | 12 | 1 | no | — |
| 72 | C2×C4 | — | 12 | 1 | no | — |
| 73 | C2×C4 | — | 12 | 1 | no | — |
| 74 | C8 | — | 3 | 1 | no | — |
| 75 | C8 | — | 12 | 1 | no | — |
| 76 | C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 77 | C2×C3 | — | 4 | 1 | no | — |
| 78 | C2×C3 | — | 32 | 1 | no | — |
| 79 | C22 | — | 3 | 1 | no | — |
| 80 | C22 | — | 4 | 1 | no | — |
| 81 | C4 | — | 3 | 1 | no | — |
| 82 | C4 | — | 12 | 1 | no | — |
| 83 | C4 | — | 24 | 1 | no | — |
| 84 | C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 85 | C3 | — | 4 | 1 | no | Sylow |
| 86 | C2 | — | 6 | 1 | no | — |
| 87 | C2 | — | 8 | 1 | no | — |
| 88 | C2 | #5415 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5403 | C2 | semidirect |
| 3. #4628 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #578⋊C3 | 2 |
| #5403 | 2 |
| #4628 | 2 |
| #2195 | 3 |
| #827 | 4 |