Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 225. C9 | #2064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#419 | 2 |
| C2×#63395 | 2 |
| C2×#63394 | 2 |
| C2×#63381 | 2 |
| #10588679 | 2 |
| #10588677 | 2 |
| #10588234 | 2 |
| #70337 | 3 |