Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
90 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#125 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #869 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #810 | C2 | 1 | 4 | yes | maximal |
| 4 | #803 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #491 | — | 3 | 1 | no | maximal, Sylow |
| 6 | C2×Dic6 | C22 | 1 | 2 | yes | — |
| 7 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 8 | C3×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 9 | C3×C42 | C22 | 1 | 1 | yes | characteristic |
| 10 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 11 | C2×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 12 | C4⋊Q8 | — | 3 | 1 | no | — |
| 13 | #125 | D3 | 1 | 1 | yes | characteristic |
| 14 | #103 | — | 3 | 4 | no | — |
| 15 | #97 | — | 3 | 1 | no | — |
| 16 | C2×C3×C4 | — | 2 | 2 | no | — |
| 17 | C2×C3×C4 | D4 | 1 | 2 | yes | — |
| 18 | C2×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 19 | C2×Dic3 | — | 2 | 2 | no | — |
| 20 | Dic6 | — | 2 | 4 | no | — |
| 21 | C3⋊C8 | — | 2 | 2 | no | — |
| 22 | C2×Q8 | — | 3 | 2 | no | — |
| 23 | C2×C8 | — | 3 | 2 | no | — |
| 24 | C4⋊C4 | — | 2 | 2 | no | — |
| 25 | C4⋊C4 | — | 6 | 2 | no | — |
| 26 | C4⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 27 | C42 | C2×D3 | 1 | 1 | yes | characteristic |
| 28 | C22×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 29 | C3×C4 | — | 2 | 2 | no | — |
| 30 | C3×C4 | — | 4 | 2 | no | — |
| 31 | C3×C4 | #41 | 1 | 2 | yes | — |
| 32 | Dic3 | — | 4 | 2 | no | — |
| 33 | Q8 | — | 6 | 4 | no | — |
| 34 | C2×C4 | — | 2 | 2 | no | — |
| 35 | C2×C4 | — | 6 | 2 | no | — |
| 36 | C2×C4 | #67 | 1 | 2 | yes | — |
| 37 | C2×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 38 | C8 | — | 6 | 2 | no | — |
| 39 | C2×C3 | #124 | 1 | 1 | yes | characteristic |
| 40 | C2×C3 | #137 | 1 | 2 | yes | — |
| 41 | C22 | C2×#67 | 1 | 1 | yes | characteristic |
| 42 | C4 | — | 2 | 2 | no | — |
| 43 | C4 | — | 4 | 2 | no | — |
| 44 | C4 | — | 12 | 2 | no | — |
| 45 | C4 | #239 | 1 | 2 | yes | — |
| 46 | C3 | #491 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 47 | C2 | #947 | 1 | 1 | yes | characteristic |
| 48 | C2 | #951 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 46. C3 | #491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#125 | 2 |
| #869 | 2 |
| #810 | 2 |
| #803 | 2 |
| #491 | 3 |