Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
360 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10588760 | C2 | semidirect |
| 3. #10588695 | C2 | semidirect |
| 4. #10588690 | C2 | semidirect |
| 5. #10588224 | C2 | semidirect |
| 6. D4⋊(C9⋊C8) | C2 | semidirect |
| 7. D4⋊(C9⋊C8) | C2 | semidirect |
| 84. D4×C9 | SD16 | semidirect |
| 239. C9 | #1654 | semidirect |
| 250. D4 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#547 | 2 |
| #10588760 | 2 |
| #10588695 | 2 |
| #10588690 | 2 |
| #10588224 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #71913 | 3 |