Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #30632090 | C2 | semidirect |
| 3. #30631897 | C2 | semidirect |
| 4. #30631433 | C2 | semidirect |
| 5. Q8⋊(C251⋊C8) | C2 | semidirect |
| 63. D4×C251 | Q16 | semidirect |
| 92. C251 | #1649 | semidirect |
| 152. D4 | #16860800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632090 | 2 |
| #30631967 | 2 |
| #30631897 | 2 |
| #30631433 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| D4⋊(C251⋊C8) | 2 |
| D4×Q8×C251 | 2 |
| #1649 | 251 |