Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #30631794 | C2 | semidirect |
| 4. #30631511 | C2 | semidirect |
| 6. #30631464 | C2 | semidirect |
| 7. #362×C251 | C2 | semidirect |
| 11. #22548661 | C4 | semidirect |
| 12. #22548658 | C4 | semidirect |
| 64. C251 | #2180 | semidirect |
| 70. #362 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632128 | 2 |
| #30631808 | 2 |
| #30631794 | 2 |
| #30631511 | 2 |
| #30631498 | 2 |
| #30631464 | 2 |
| #362×C251 | 2 |
| #2180 | 251 |