Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
669 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 669 conjugacy classes of subgroups — too many to draw. Only its 150 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. #10589827 | C2 | semidirect |
| 2. #10589818 | C2 | semidirect |
| 3. C9×#486 | C2 | semidirect |
| 4. #10588760 | C2 | semidirect |
| 5. #10588755 | C2 | semidirect |
| 6. #10588465 | C2 | semidirect |
| 7. #10588462 | C2 | semidirect |
| 8. #10588376 | C2 | semidirect |
| 9. C4×#3663 | C2 | semidirect |
| 131. C9⋊C8 | #41 | semidirect |
| 137. #486 | D9 | semidirect |
| 302. C9 | #3184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589827 | 2 |
| #10589818 | 2 |
| C9×#486 | 2 |
| #10588760 | 2 |
| #10588755 | 2 |
| #10588465 | 2 |
| #10588462 | 2 |
| #10588376 | 2 |
| C4×#3663 | 2 |
| #81560 | 3 |