Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
245 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 90 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. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 3. C3×C4×C3⋊C16 | C2 | semidirect |
| 19. C4×C3⋊C16 | D3 | semidirect |
| 55. C3×D12 | C16 | semidirect |
| 128. D12 | C3⋊C16 | semidirect |
| 184. C32 | D4⋊C16 | semidirect |
| 220. C3 | #67503 | semidirect |
| 221. C3 | D4⋊(C3⋊C16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D12 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| C3×C4×C3⋊C16 | 2 |
| D4⋊(C3⋊C16) | 3 |
| #67503 | 3 |