Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 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. Q8×#14523266 | C2 | semidirect |
| 3. #30654283 | C2 | semidirect |
| 4. #30654278 | C2 | semidirect |
| 6. C8×#14523266 | C2 | semidirect |
| 18. #22550850 | C4 | semidirect |
| 19. #22550849 | C4 | semidirect |
| 20. #22550848 | C4 | semidirect |
| 22. SD16×C509 | C4 | semidirect |
| 31. Dic1018 | C2×C4 | semidirect |
| 36. #16861325 | C2×C4 | semidirect |
| 37. Q8×C509 | C2×C4 | semidirect |
| 39. C8×C509 | C2×C4 | semidirect |
| 48. #14523266 | SD16 | direct (N × H) |
| 58. C509 | C4×SD16 | semidirect |
| 73. SD16 | #14523266 | direct (N × H) |
| 85. Q8 | C2×#14523266 | semidirect |
| 98. C8 | C2×#14523266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14523266 | 2 |
| D4×#14523266 | 2 |
| #30654283 | 2 |
| #30654278 | 2 |
| #30654277 | 2 |
| C8×#14523266 | 2 |
| SD16×D509 | 2 |
| C4×SD16 | 509 |