Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
793 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 793 conjugacy classes of subgroups — too many to draw. Only its 236 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. #10590314 | C2 | semidirect |
| 5. #10590312 | C2 | semidirect |
| 6. #10590309 | C2 | semidirect |
| 34. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 185. C32 | #3160 | semidirect |
| 212. C3 | #83339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5470 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10591138 | 2 |
| #10590314 | 2 |
| #10590312 | 2 |
| #10590309 | 2 |
| #83339 | 3 |