Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
494 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #10593561 | C2 | direct (N × H) |
| 29. C2×C32×Q8 | Q8 | semidirect |
| 32. Q8×C3⋊D3 | Q8 | semidirect |
| 37. C2×#634 | Q8 | semidirect |
| 63. C32×Q8 | C2×Q8 | semidirect |
| 77. #634 | C2×Q8 | semidirect |
| 142. C2×C32 | #475 | semidirect |
| 144. C3⋊D3 | #475 | semidirect |
| 155. C2×Q8 | PSU(3,𝔽2) | semidirect |
| 185. C32 | C2×#475 | semidirect |
| 193. Q8 | C2×PSU(3,𝔽2) | semidirect |
| 237. C2 | #10593561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×#63784 | 2 |
| #10593561 | 2 |
| C2×#63745 | 2 |
| C2×#63744 | 2 |
| C2×#475 | 9 |