Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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. #30654248 | C2 | semidirect |
| 3. #30654245 | C2 | semidirect |
| 4. #30654215 | C2 | semidirect |
| 5. #30654143 | C2 | semidirect |
| 6. #30654133 | C2 | semidirect |
| 7. #104×C509 | C2 | semidirect |
| 61. C509 | #456 | semidirect |
| 68. #104 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654262 | 2 |
| #30654248 | 2 |
| #30654245 | 2 |
| #30654215 | 2 |
| #30654143 | 2 |
| #30654133 | 2 |
| #104×C509 | 2 |
| #456 | 509 |