Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 345 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. #10588154 | C2 | semidirect |
| 224. C9 | #2135 | 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 |
| #10588915 | 2 |
| #10588154 | 2 |
| #70150 | 3 |