Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 449 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 |
|---|---|---|
| 3. C3×#4457 | C2 | semidirect |
| 4. #10589098 | C2 | semidirect |
| 21. #4457 | D3 | semidirect |
| 68. C32×C8 | M16 | semidirect |
| 70. C3⋊(C3⋊C8) | M16 | semidirect |
| 152. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 199. C32 | #1566 | semidirect |
| 215. C8 | #3712 | semidirect |
| 236. C3 | #68529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| #10590340 | 2 |
| C3×#4457 | 2 |
| #10589098 | 2 |
| #68529 | 3 |