Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
567 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 567 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 3. #10588807 | C2 | semidirect |
| 4. #10588788 | C2 | semidirect |
| 5. #10588405 | C2 | semidirect |
| 6. #10588403 | C2 | semidirect |
| 216. C9 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589927 | 2 |
| C9×#408 | 2 |
| #10588807 | 2 |
| #10588788 | 2 |
| #10588405 | 2 |
| #10588403 | 2 |
| #78682 | 3 |