Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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×M16 | C2 | semidirect |
| 3. #63486 | C2 | semidirect |
| 4. C2×#3664 | C2 | semidirect |
| 5. #63380 | C2 | semidirect |
| 6. #63378 | C2 | semidirect |
| 7. #63376 | C2 | semidirect |
| 44. C8×C9 | D4 | semidirect |
| 73. C2×M16 | D9 | semidirect |
| 126. C9 | #468 | semidirect |
| 142. C8 | #611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×M16 | 2 |
| #63492 | 2 |
| #63486 | 2 |
| C2×#3664 | 2 |
| #63380 | 2 |
| #63378 | 2 |
| #63376 | 2 |
| #5134 | 3 |