Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
180 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10588538 | C2 | semidirect |
| 5. #10588190 | C2 | semidirect |
| 6. #10588188 | C2 | semidirect |
| 7. #10588164 | C2 | semidirect |
| 150. C9 | #2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588876 | 2 |
| #10588538 | 2 |
| C9×#360 | 2 |
| #10588243 | 2 |
| #10588190 | 2 |
| #10588188 | 2 |
| #10588164 | 2 |
| #69247 | 3 |