Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
925 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 925 conjugacy classes of subgroups — too many to draw. Only its 272 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×Q8×C3⋊C8 | C2 | semidirect |
| 5. #10590296 | C2 | semidirect |
| 23. Q8×C3⋊C8 | D3 | semidirect |
| 44. #3712 | Q8 | direct (N × H) |
| 70. C32×Q8 | M16 | semidirect |
| 83. C3×C3⋊C8 | C2×Q8 | semidirect |
| 148. C3×Q8 | ΓL(1,𝔽25) | semidirect |
| 174. C3⋊C8 | D3×Q8 | semidirect |
| 218. C32 | Q8×M16 | semidirect |
| 221. Q8 | #3712 | direct (N × H) |
| 254. C3 | Q8×ΓL(1,𝔽25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C3⋊D3 | 2 |
| C3×Q8×C3⋊C8 | 2 |
| #10590340 | 2 |
| C4×#3712 | 2 |
| #10590296 | 2 |
| Q8×ΓL(1,𝔽25) | 3 |