Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×C8×D12 | C2 | semidirect |
| 3. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10589100 | C2 | semidirect |
| 5. #10589080 | C2 | semidirect |
| 19. C8×D12 | D3 | semidirect |
| 37. #3713 | C8 | direct (N × H) |
| 63. C3×D12 | C2×C8 | semidirect |
| 67. C32×C8 | D8 | semidirect |
| 70. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 137. D12 | D3×C8 | semidirect |
| 144. C3×C8 | #213 | semidirect |
| 189. C32 | C8×D8 | semidirect |
| 204. C8 | #3713 | direct (N × H) |
| 224. C3 | C8×#213 | 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×#3713 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #10589100 | 2 |
| #10589080 | 2 |
| C8×#213 | 3 |