Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #10588152 | C2 | semidirect |
| 7. C22×Dic18 | C4 | semidirect |
| 11. #63497 | C4 | semidirect |
| 14. #63488 | C4 | semidirect |
| 226. C9 | #2123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589927 | 2 |
| C9×#413 | 2 |
| #10588920 | 2 |
| #10588152 | 2 |
| #70147 | 3 |