Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
669 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 669 conjugacy classes of subgroups — too many to draw. Only its 174 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. #10589579 | C2 | semidirect |
| 2. C4×C9×M16 | C2 | semidirect |
| 3. #10588817 | C2 | semidirect |
| 4. #10588392 | C2 | semidirect |
| 5. #10588377 | C2 | semidirect |
| 6. #10588376 | C2 | semidirect |
| 7. #10588360 | C2 | semidirect |
| 85. C8×C9 | #41 | semidirect |
| 92. C4×M16 | D9 | semidirect |
| 192. C9 | #3184 | semidirect |
| 209. C8 | #3697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589579 | 2 |
| C4×C9×M16 | 2 |
| #10588817 | 2 |
| #10588392 | 2 |
| #10588377 | 2 |
| #10588376 | 2 |
| #10588360 | 2 |
| #78535 | 3 |