Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
586 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #10593835 | C2 | semidirect |
| 3. Q8×#622 | C2 | semidirect |
| 4. #10593756 | C2 | semidirect |
| 6. #10593750 | C2 | semidirect |
| 45. #3787 | Q8 | semidirect |
| 206. C32 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596199 | 2 |
| #10593835 | 2 |
| Q8×#622 | 2 |
| #10593756 | 2 |
| #10593755 | 2 |
| #10593750 | 2 |
| #10593748 | 2 |
| #10593728 | 2 |
| C4×#3787 | 2 |
| #2960 | 9 |