Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. #10589815 | C2 | semidirect |
| 3. #10588752 | C2 | semidirect |
| 4. #10588221 | C2 | semidirect |
| 5. #10588133 | C2 | semidirect |
| 157. C9 | #1620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589815 | 2 |
| C9×#493 | 2 |
| #10588752 | 2 |
| #10588221 | 2 |
| #10588133 | 2 |
| #71284 | 3 |