Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×C3×SD32 | C2 | semidirect |
| 3. #5188 | C2 | semidirect |
| 4. C2×#828 | C2 | semidirect |
| 5. #4562 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. (C2×D3)⋊C16 | C2 | semidirect |
| 10. C2×C3×Q16 | C22 | semidirect |
| 19. C2×C3×C16 | C22 | semidirect |
| 22. #818 | C22 | semidirect |
| 23. C2×C3⋊C16 | C22 | semidirect |
| 26. C2×SD32 | D3 | semidirect |
| 56. C2×Q16 | C2×D3 | semidirect |
| 67. C2×C16 | C2×D3 | semidirect |
| 126. C2×D3 | SD32 | semidirect |
| 176. C3 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D8 | 2 |
| C2×C3×SD32 | 2 |
| #5188 | 2 |
| C2×#828 | 2 |
| #4562 | 2 |
| #4509 | 2 |
| (C2×D3)⋊C16 | 2 |
| #2187 | 3 |