Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548738 | C2 | semidirect |
| 2. C2×#22548736 | C2 | semidirect |
| 3. C2×#22548734 | C2 | semidirect |
| 4. #30632236 | C2 | semidirect |
| 5. #30632071 | C2 | semidirect |
| 6. #30632069 | C2 | semidirect |
| 7. #30632065 | C2 | semidirect |
| 8. #30632062 | C2 | semidirect |
| 9. #30632058 | C2 | semidirect |
| 10. C4×C8×D251 | C2 | semidirect |
| 11. #495×C251 | C2 | semidirect |
| 62. C8×D251 | D4 | semidirect |
| 63. C8×D251 | D4 | semidirect |
| 119. Dic251 | #135 | semidirect |
| 125. C251 | #3147 | semidirect |
| 133. #495 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| C2×#22548736 | 2 |
| C2×#22548734 | 2 |
| #30632236 | 2 |
| #30632071 | 2 |
| #30632069 | 2 |
| #30632065 | 2 |
| #30632062 | 2 |
| #30632058 | 2 |
| C4×C8×D251 | 2 |
| #495×C251 | 2 |
| #3147 | 251 |