Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 2. C9×#499 | C2 | semidirect |
| 3. #10588744 | C2 | semidirect |
| 5. #10588558 | C2 | semidirect |
| 7. #10588538 | C2 | semidirect |
| 9. #10588363 | C2 | semidirect |
| 98. #499 | D9 | direct (N × H) |
| 167. D9 | #499 | direct (N × H) |
| 197. C9 | C2×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×#125 | 2 |
| C9×#499 | 2 |
| #10588744 | 2 |
| D9×#107 | 2 |
| #10588558 | 2 |
| D9×#106 | 2 |
| #10588538 | 2 |
| C4×C8×D9 | 2 |
| #10588363 | 2 |
| D3×#499 | 3 |