Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
973 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 973 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. #10593970 | C2 | semidirect |
| 2. #10592394 | C2 | semidirect |
| 3. C3×C4×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#4680 | C2 | semidirect |
| 5. #10590835 | C2 | semidirect |
| 6. #10590768 | C2 | semidirect |
| 7. #10590281 | C2 | semidirect |
| 39. C4×ΓL(1,𝔽25) | D3 | semidirect |
| 40. #4680 | D3 | semidirect |
| 112. C32×C8 | #41 | semidirect |
| 232. C3×C8 | #235 | semidirect |
| 233. C3×C8 | #239 | semidirect |
| 287. C32 | #3184 | semidirect |
| 304. C8 | #3799 | semidirect |
| 328. C3 | #78535 | semidirect |
| 329. C3 | #81888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593970 | 2 |
| #10592394 | 2 |
| C3×C4×ΓL(1,𝔽25) | 2 |
| C3×#4680 | 2 |
| #10590835 | 2 |
| #10590768 | 2 |
| #10590281 | 2 |
| #81888 | 3 |
| #78535 | 3 |