Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
| 4. #63394 | C2 | semidirect |
| 5. #63372 | C2 | semidirect |
| 54. C2×Q16 | D9 | semidirect |
| 90. C9 | #473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Q16 | 2 |
| #63505 | 2 |
| #63464 | 2 |
| #63394 | 2 |
| #63372 | 2 |
| #5192 | 3 |