Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30632085 | C2 | semidirect |
| 5. #30631435 | C2 | semidirect |
| 6. #30631434 | C2 | semidirect |
| 7. #334×C251 | C2 | semidirect |
| 59. C8×C251 | SD16 | semidirect |
| 76. C251 | #1671 | semidirect |
| 82. #334 | D251 | semidirect |
| 136. C8 | #16860799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632085 | 2 |
| #30631978 | 2 |
| #30631893 | 2 |
| C8×D1004 | 2 |
| #30631435 | 2 |
| #30631434 | 2 |
| #334×C251 | 2 |
| #1671 | 251 |