Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5812 | C2 | semidirect |
| 4. C3×#419 | C2 | semidirect |
| 6. #5122 | C2 | semidirect |
| 7. #4998 | C2 | semidirect |
| 8. #4817 | C2 | semidirect |
| 9. #4788 | C2 | semidirect |
| 16. Q8×Dic3 | C22 | semidirect |
| 17. C2×#215 | C4 | semidirect |
| 27. C3×#103 | C22 | semidirect |
| 29. #815 | C22 | semidirect |
| 30. C8×Dic3 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 32. #807 | C22 | semidirect |
| 39. #419 | D3 | semidirect |
| 45. C2×C3×Q8 | C2×C4 | semidirect |
| 61. #215 | C2×C4 | semidirect |
| 62. #215 | C2×C4 | semidirect |
| 70. C2×C3⋊C8 | C2×C4 | semidirect |
| 91. #103 | C2×D3 | semidirect |
| 121. C2×Q8 | C4×D3 | semidirect |
| 202. C3 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5812 | 2 |
| C22×#215 | 2 |
| #5521 | 2 |
| C3×#419 | 2 |
| #5131 | 2 |
| #5122 | 2 |
| #4998 | 2 |
| #4817 | 2 |
| #4788 | 2 |
| #2949 | 3 |