Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10588521 | C2 | semidirect |
| 3. #10588517 | C2 | semidirect |
| 4. C9×#331 | C2 | semidirect |
| 5. #10588221 | C2 | semidirect |
| 6. #10588163 | C2 | semidirect |
| 7. #10588163 | C2 | semidirect |
| 19. C9×C4⋊C8 | C22 | semidirect |
| 20. C9×C4⋊C8 | C22 | semidirect |
| 24. C4⋊(C9⋊C8) | C22 | semidirect |
| 25. C4⋊(C9⋊C8) | C22 | semidirect |
| 118. #331 | D9 | semidirect |
| 178. C4⋊C8 | C2×D9 | semidirect |
| 179. C4⋊C8 | C2×D9 | semidirect |
| 268. C9 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×#127 | 2 |
| #10588521 | 2 |
| #10588517 | 2 |
| C9×#331 | 2 |
| #10588221 | 2 |
| #10588163 | 2 |
| #68383 | 3 |