Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #30631591 | C2 | semidirect |
| 3. #30631578 | C2 | semidirect |
| 4. #30631577 | C2 | semidirect |
| 6. #30631558 | C2 | semidirect |
| 7. #30631555 | C2 | semidirect |
| 8. C4×(C2×D251)⋊C4 | C2 | semidirect |
| 9. C4×C4⋊C4×C251 | C2 | semidirect |
| 13. #22548703 | C4 | semidirect |
| 34. C2×Dic502 | C2×C4 | semidirect |
| 47. (C2×D251)⋊C4 | C2×C4 | semidirect |
| 48. (C2×D251)⋊C4 | C2×C4 | semidirect |
| 58. C42×C251 | C2×C4 | semidirect |
| 118. C251 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D251 | semidirect |
| 177. C42 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548703 | 2 |
| #30631591 | 2 |
| #30631578 | 2 |
| #30631577 | 2 |
| #30631565 | 2 |
| #30631558 | 2 |
| #30631555 | 2 |
| C4×(C2×D251)⋊C4 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #2337 | 251 |