Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
810 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 5. #10593295 | C2 | direct (N × H) |
| 53. C2×#157 | Q16 | semidirect |
| 96. #157 | C2×Q16 | semidirect |
| 136. C2×C32 | #494 | semidirect |
| 138. C3⋊D3 | #494 | semidirect |
| 172. C32 | C2×#494 | semidirect |
| 209. C2 | #10593295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64228 | 2 |
| C2×#64222 | 2 |
| C2×#63802 | 2 |
| C2×C8×#157 | 2 |
| #10593295 | 2 |
| C2×#494 | 9 |