Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 214 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. C9×#423 | C2 | semidirect |
| 4. M16×Dic9 | C2 | semidirect |
| 5. #10588604 | C2 | semidirect |
| 6. #10588524 | C2 | semidirect |
| 17. C9×C4⋊C8 | C22 | semidirect |
| 19. #63375 | C22 | semidirect |
| 20. C8×Dic9 | C22 | semidirect |
| 21. C4⋊(C9⋊C8) | C22 | semidirect |
| 84. #423 | D9 | semidirect |
| 128. C4⋊C8 | C2×D9 | semidirect |
| 186. C9 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63434 | 2 |
| C9×#423 | 2 |
| #10588808 | 2 |
| M16×Dic9 | 2 |
| #10588604 | 2 |
| #10588524 | 2 |
| #79039 | 3 |