Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
772 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10595412 | C2 | semidirect |
| 2. Q8×#622 | C2 | semidirect |
| 3. #10593418 | C2 | semidirect |
| 4. #10593417 | C2 | semidirect |
| 5. C4×#3774 | C2 | semidirect |
| 41. C32×Q8 | D8 | semidirect |
| 52. #622 | #41 | semidirect |
| 138. C32 | #3391 | semidirect |
| 140. Q8 | #3774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595412 | 2 |
| Q8×#622 | 2 |
| #10593418 | 2 |
| #10593417 | 2 |
| C4×#3774 | 2 |
| #3391 | 9 |