Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #30631730 | C2 | semidirect |
| 4. #30631556 | C2 | semidirect |
| 5. #30631456 | C2 | semidirect |
| 6. #30631446 | C2 | semidirect |
| 15. #22548642 | C4 | semidirect |
| 31. #16860794 | C2×C4 | semidirect |
| 38. C4×Dic251 | C2×C4 | semidirect |
| 69. Q8×C251 | C4⋊C4 | semidirect |
| 73. D4×C251 | C4⋊C4 | semidirect |
| 112. C251 | #1859 | semidirect |
| 175. Q8 | Dic251⋊C4 | semidirect |
| 179. D4 | Dic251⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631730 | 2 |
| C2×#22548642 | 2 |
| #30631688 | 2 |
| #30631556 | 2 |
| #30631456 | 2 |
| #30631446 | 2 |
| #520×C251 | 2 |
| #1859 | 251 |