Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #30654303 | C2 | semidirect |
| 2. #30654302 | C2 | semidirect |
| 3. #30654286 | C2 | semidirect |
| 4. #30654280 | C2 | semidirect |
| 5. #30654279 | C2 | semidirect |
| 6. #30654269 | C2 | semidirect |
| 18. #22550851 | C4 | semidirect |
| 19. #22550850 | C4 | semidirect |
| 20. #22550846 | C4 | semidirect |
| 22. SD16×C509 | C4 | semidirect |
| 51. C509 | #444 | semidirect |
| 64. SD16 | #14523266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654303 | 2 |
| #30654302 | 2 |
| #30654286 | 2 |
| #30654280 | 2 |
| #30654279 | 2 |
| #30654269 | 2 |
| #30654236 | 2 |
| #444 | 509 |