Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3108 conjugacy classes of subgroups; only the 689 normal subgroups are shown.
This group has 3108 conjugacy classes of subgroups — too many to draw. Only its 689 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 |
|---|---|---|
| 1. C23×C32×Q8 | C2 | semidirect |
| 3. #10592930 | C2 | direct (N × H) |
| 4. C2×#63658 | C2 | semidirect |
| 8. C22×C32×Q8 | C22 | semidirect |
| 13. #63658 | C22 | semidirect |
| 14. C23×C3×Q8 | D3 | semidirect |
| 21. C23×C3⋊D3 | Q8 | semidirect |
| 35. C22×C3×Q8 | C2×D3 | semidirect |
| 50. C22×C3⋊D3 | C2×Q8 | semidirect |
| 58. C23×Q8 | C3⋊D3 | semidirect |
| 90. C22×Q8 | C2×C3⋊D3 | semidirect |
| 113. C2×C32 | #393 | semidirect |
| 144. C32 | C2×#393 | semidirect |
| 162. C2×C3 | #5231 | semidirect |
| 179. C3 | C2×#5231 | semidirect |
| 181. C2 | #10592930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C22×#3752 | 2 |
| #10592930 | 2 |
| C2×#63658 | 2 |
| C2×#5231 | 3 |