Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 108 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. #10590329 | C2 | semidirect |
| 3. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C3×#4459 | C2 | semidirect |
| 5. #10589100 | C2 | semidirect |
| 22. #4459 | D3 | semidirect |
| 36. #3713 | C8 | semidirect |
| 63. C3×D12 | C2×C8 | semidirect |
| 69. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 70. C3⋊(C3⋊C8) | D8 | semidirect |
| 137. D12 | D3×C8 | semidirect |
| 189. C32 | C8×D8 | semidirect |
| 224. C3 | #68148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3713 | 2 |
| #10590329 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C3×#4459 | 2 |
| #10589100 | 2 |
| #68148 | 3 |