Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
941 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 941 conjugacy classes of subgroups — too many to draw. Only its 188 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. #10593897 | C2 | semidirect |
| 2. #10592379 | C2 | semidirect |
| 3. C3×#4695 | C2 | semidirect |
| 4. C3×C4×ΓL(1,𝔽25) | C2 | semidirect |
| 5. #10590836 | C2 | semidirect |
| 6. #10590771 | C2 | semidirect |
| 7. #10590273 | C2 | semidirect |
| 35. #4695 | D3 | semidirect |
| 37. C4×ΓL(1,𝔽25) | D3 | semidirect |
| 112. C32×C8 | #41 | semidirect |
| 229. C3×C8 | #235 | semidirect |
| 230. C3×C8 | #237 | semidirect |
| 282. C32 | #3184 | semidirect |
| 299. C8 | #3795 | semidirect |
| 322. C3 | #78535 | semidirect |
| 323. C3 | #81777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593897 | 2 |
| #10592379 | 2 |
| C3×#4695 | 2 |
| C3×C4×ΓL(1,𝔽25) | 2 |
| #10590836 | 2 |
| #10590771 | 2 |
| #10590273 | 2 |
| #81777 | 3 |
| #78535 | 3 |