Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D509 | C2 | semidirect |
| 2. C2×#22550849 | C2 | semidirect |
| 4. #30654140 | C2 | semidirect |
| 5. #30654139 | C2 | semidirect |
| 6. #30654127 | C2 | semidirect |
| 7. C2×SD16×C509 | C2 | semidirect |
| 26. Dic1018 | D4 | semidirect |
| 37. Q8×C509 | D4 | semidirect |
| 49. C2×D509 | SD16 | semidirect |
| 61. C509 | #448 | semidirect |
| 65. C2×SD16 | D509 | semidirect |
| 91. Q8 | C22⋊D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D509 | 2 |
| C2×#22550849 | 2 |
| #30654186 | 2 |
| #30654140 | 2 |
| #30654139 | 2 |
| #30654127 | 2 |
| C2×SD16×C509 | 2 |
| #448 | 509 |