Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#63471 | C2 | semidirect |
| 3. C2×#63384 | C2 | semidirect |
| 4. #10588653 | C2 | semidirect |
| 5. C9×#343 | C2 | semidirect |
| 42. C2×Dic18 | D4 | semidirect |
| 44. C9×M16 | D4 | semidirect |
| 98. #343 | D9 | semidirect |
| 206. M16 | D36 | semidirect |
| 226. C9 | #2007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63471 | 2 |
| #10589612 | 2 |
| C2×#63384 | 2 |
| #10588653 | 2 |
| C9×#343 | 2 |
| #69009 | 3 |