Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10588887 | C2 | semidirect |
| 3. #10588202 | C2 | semidirect |
| 14. #63389 | C22 | semidirect |
| 65. C23×C9 | M16 | semidirect |
| 209. C9 | #1462 | semidirect |
| 224. C23 | #3667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×C22⋊C4 | 2 |
| #10588887 | 2 |
| #10588202 | 2 |
| #71539 | 3 |