Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 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. C23×D12 | C2 | semidirect |
| 2. C2×#930 | C2 | semidirect |
| 3. C22×D24 | C2 | semidirect |
| 4. C2×C3×C22⋊C8 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. #4732 | C2 | direct (N × H) |
| 15. C22×D12 | C22 | semidirect |
| 16. C22×D12 | C22 | semidirect |
| 17. C22×C3×C8 | C22 | semidirect |
| 19. #930 | C22 | semidirect |
| 21. C2×C4⋊Dic3 | C22 | semidirect |
| 23. C2×D24 | C22 | semidirect |
| 24. C3×C22⋊C8 | C22 | semidirect |
| 25. #821 | C22 | semidirect |
| 31. C2×C22⋊C8 | D3 | semidirect |
| 55. C2×D12 | D4 | semidirect |
| 57. C2×D12 | C23 | semidirect |
| 59. C2×C3×C8 | C23 | semidirect |
| 62. C4⋊Dic3 | C23 | semidirect |
| 75. C22×C8 | C2×D3 | semidirect |
| 81. C22⋊C8 | C2×D3 | semidirect |
| 84. C23×C3 | D8 | semidirect |
| 114. D12 | C2×D4 | semidirect |
| 144. C2×C8 | C22×D3 | semidirect |
| 153. C22×C3 | C2×D8 | semidirect |
| 183. C23 | D24 | semidirect |
| 204. C2×C3 | #447 | semidirect |
| 224. C22 | C2×D24 | semidirect |
| 231. C3 | C2×#447 | semidirect |
| 235. C2 | #4732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C2×#930 | 2 |
| C22×D24 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| #4732 | 2 |
| C2×#447 | 3 |