Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 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×#22550848 | C2 | semidirect |
| 2. C22×#16861325 | C2 | semidirect |
| 4. #30654146 | C2 | semidirect |
| 5. #30654139 | C2 | semidirect |
| 6. #30654135 | C2 | semidirect |
| 7. C22⋊Q8×C509 | C2 | semidirect |
| 27. #16861325 | D4 | semidirect |
| 39. C22×C509 | SD16 | semidirect |
| 55. C509 | #465 | semidirect |
| 59. C22⋊Q8 | D509 | semidirect |
| 98. C22 | #22550848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550848 | 2 |
| C22×#16861325 | 2 |
| #30654189 | 2 |
| #30654146 | 2 |
| #30654139 | 2 |
| #30654135 | 2 |
| C22⋊Q8×C509 | 2 |
| #465 | 509 |