Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×#4681 | C2 | semidirect |
| 4. #10590309 | C2 | semidirect |
| 5. #10590290 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 34. #4681 | D3 | semidirect |
| 252. C32 | #1708 | semidirect |
| 291. C3 | #71181 | semidirect |
| 292. C3 | #71213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4694 | 2 |
| C3×#4681 | 2 |
| #10590375 | 2 |
| #10590309 | 2 |
| #10590290 | 2 |
| #10590277 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71213 | 3 |
| #71181 | 3 |