Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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. #10595941 | C2 | semidirect |
| 5. #10589425 | C2 | semidirect |
| 6. #10589423 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 35. C2×C32×Q8 | Q8 | semidirect |
| 37. C2×C32×D4 | Q8 | semidirect |
| 115. C2×C3×Q8 | Dic6 | semidirect |
| 117. C2×C3×D4 | Dic6 | semidirect |
| 209. C2×Q8 | #634 | semidirect |
| 211. C2×D4 | #634 | semidirect |
| 251. C32 | #2031 | semidirect |
| 299. C3 | #70368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595941 | 2 |
| C2×C32×#104 | 2 |
| #10592939 | 2 |
| #10592935 | 2 |
| #10589425 | 2 |
| #10589423 | 2 |
| #10589389 | 2 |
| #70368 | 3 |