Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1308 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1308 conjugacy classes of subgroups — too many to draw. Only its 345 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. C2×C32×C4⋊Q8 | C2 | semidirect |
| 3. #10592788 | C2 | direct (N × H) |
| 4. C2×#63637 | C2 | semidirect |
| 6. C2×#63630 | C2 | semidirect |
| 12. C32×C4⋊Q8 | C22 | semidirect |
| 21. #63637 | C22 | semidirect |
| 23. #63630 | C22 | semidirect |
| 24. C2×C3×C4⋊Q8 | D3 | semidirect |
| 58. C3×C4⋊Q8 | C2×D3 | semidirect |
| 92. C2×C4⋊Q8 | C3⋊D3 | semidirect |
| 140. C4⋊Q8 | C2×C3⋊D3 | semidirect |
| 173. C2×C32 | #489 | semidirect |
| 215. C32 | C2×#489 | semidirect |
| 238. C2×C3 | #5089 | semidirect |
| 257. C3 | C2×#5089 | semidirect |
| 259. C2 | #10592788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊Q8 | 2 |
| C2×#64084 | 2 |
| #10592788 | 2 |
| C2×#63637 | 2 |
| C2×#63636 | 2 |
| C2×#63630 | 2 |
| C2×#5089 | 3 |