Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22548736 | C2 | semidirect |
| 2. #30632341 | C2 | semidirect |
| 3. #30632340 | C2 | semidirect |
| 4. #30632066 | C2 | semidirect |
| 5. #30631927 | C2 | semidirect |
| 6. #30631893 | C2 | semidirect |
| 7. #30631852 | C2 | semidirect |
| 8. #30631846 | C2 | semidirect |
| 9. C4×#16860795 | C2 | semidirect |
| 10. #30631752 | C2 | semidirect |
| 11. #461×C251 | C2 | semidirect |
| 58. #16860795 | D4 | semidirect |
| 126. C4×C251 | #135 | semidirect |
| 138. C251 | #3283 | semidirect |
| 146. #461 | D251 | semidirect |
| 268. C4 | #22548736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548736 | 2 |
| #30632341 | 2 |
| #30632340 | 2 |
| #30632066 | 2 |
| #30631927 | 2 |
| #30631893 | 2 |
| #30631852 | 2 |
| #30631846 | 2 |
| C4×#16860795 | 2 |
| #30631752 | 2 |
| #461×C251 | 2 |
| #3283 | 251 |