Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1026 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 6. #10593556 | C2 | direct (N × H) |
| 31. C22×#157 | Q8 | semidirect |
| 39. C22×C32×C4 | Q8 | semidirect |
| 40. C22×C3⋊Dic3 | Q8 | semidirect |
| 43. C2×C4×C3⋊D3 | Q8 | semidirect |
| 69. C2×#157 | C2×Q8 | semidirect |
| 72. C2×C32×C4 | C2×Q8 | semidirect |
| 74. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 137. C2×C32 | #395 | semidirect |
| 140. C3⋊D3 | #395 | semidirect |
| 167. C22×C4 | PSU(3,𝔽2) | semidirect |
| 184. C32 | C2×#395 | semidirect |
| 213. C2×C4 | C2×PSU(3,𝔽2) | semidirect |
| 244. C2 | #10593556 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2) | 2 |
| C22×C4⋊#157 | 2 |
| C22×#3777 | 2 |
| C2×#63781 | 2 |
| C2×#63747 | 2 |
| #10593556 | 2 |
| C2×#395 | 9 |