Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #5486 | C2 | semidirect |
| 3. C2×#806 | C2 | semidirect |
| 4. C2×#806 | C2 | semidirect |
| 5. C2×#806 | C2 | semidirect |
| 6. C3×#342 | C2 | semidirect |
| 7. #4527 | C2 | semidirect |
| 19. #886 | C4 | semidirect |
| 21. #882 | C4 | semidirect |
| 34. #342 | D3 | semidirect |
| 36. C23×D3 | C2×C4 | semidirect |
| 55. C22×Dic3 | C2×C4 | semidirect |
| 63. C3×C22⋊C4 | C2×C4 | semidirect |
| 64. C3×C22⋊C4 | D4 | semidirect |
| 68. #217 | D4 | semidirect |
| 173. C22⋊C4 | C4×D3 | semidirect |
| 174. C22⋊C4 | D12 | semidirect |
| 286. C3 | #1913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5493 | 2 |
| #5486 | 2 |
| C2×#806 | 2 |
| C3×#342 | 2 |
| #4527 | 2 |
| #1913 | 3 |