Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 167 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. #10593532 | C2 | direct (N × H) |
| 40. C2×C32×C8 | Q8 | semidirect |
| 41. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 42. C8×C3⋊D3 | Q8 | semidirect |
| 64. C32×C8 | C2×Q8 | semidirect |
| 65. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 113. C2×C32 | #446 | semidirect |
| 115. C3⋊D3 | #446 | semidirect |
| 134. C2×C8 | PSU(3,𝔽2) | semidirect |
| 150. C32 | C2×#446 | semidirect |
| 170. C8 | C2×PSU(3,𝔽2) | semidirect |
| 193. C2 | #10593532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×#63767 | 2 |
| C2×C8×#157 | 2 |
| C2×#63744 | 2 |
| #10593532 | 2 |
| C2×#446 | 9 |