Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 80 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. C9×#537 | C2 | semidirect |
| 2. #10588719 | C2 | semidirect |
| 3. #10588671 | C2 | semidirect |
| 4. #10588214 | C2 | semidirect |
| 5. #10588205 | C2 | semidirect |
| 85. C2×C4×C9 | D8 | semidirect |
| 93. #537 | D9 | semidirect |
| 236. C9 | #1598 | semidirect |
| 264. C2×C4 | #3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#537 | 2 |
| #10588719 | 2 |
| #10588671 | 2 |
| #10588214 | 2 |
| #10588205 | 2 |
| #71878 | 3 |