Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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. C9×#124 | C2 | semidirect |
| 2. C2×#3675 | C2 | semidirect |
| 4. C4×D36 | C2 | semidirect |
| 5. #63395 | C2 | semidirect |
| 6. #63392 | C2 | semidirect |
| 7. C4⋊(C9⋊C8) | C2 | semidirect |
| 74. #124 | D9 | semidirect |
| 126. C9 | #463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#124 | 2 |
| C2×#3675 | 2 |
| C2×#3673 | 2 |
| C4×D36 | 2 |
| #63395 | 2 |
| #63392 | 2 |
| C4⋊(C9⋊C8) | 2 |
| #5057 | 3 |