Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
537 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 158 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. C9×#498 | C2 | semidirect |
| 3. #10588766 | C2 | semidirect |
| 5. #10588533 | C2 | semidirect |
| 7. #10588365 | C2 | semidirect |
| 82. #498 | D9 | semidirect |
| 176. C9 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589830 | 2 |
| C9×#498 | 2 |
| #10588766 | 2 |
| #10588547 | 2 |
| #10588533 | 2 |
| C4×#3663 | 2 |
| #10588365 | 2 |
| #81889 | 3 |