Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
123 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×C9×Q16 | C2 | semidirect |
| 3. #63388 | C2 | semidirect |
| 4. #63387 | C2 | semidirect |
| 5. #63371 | C2 | semidirect |
| 48. C2×Q16 | D9 | semidirect |
| 80. C9 | #510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Q16 | 2 |
| #63467 | 2 |
| #63388 | 2 |
| #63387 | 2 |
| #63371 | 2 |
| #5179 | 3 |