Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22548740 | C2 | semidirect |
| 2. C2×#22548712 | C2 | semidirect |
| 3. #30631887 | C2 | semidirect |
| 4. #30631882 | C2 | semidirect |
| 5. #30631711 | C2 | semidirect |
| 6. #30631691 | C2 | semidirect |
| 7. C4×#41×C251 | C2 | semidirect |
| 11. C2×#16860797 | C22 | semidirect |
| 12. C2×#16860795 | C22 | semidirect |
| 17. C4⋊(C251⋊C8) | C22 | semidirect |
| 18. #22548635 | C22 | semidirect |
| 20. C4×Q8×C251 | C22 | semidirect |
| 22. C4×D4×C251 | C22 | semidirect |
| 40. #41×C251 | D4 | semidirect |
| 69. Q8×C251 | C2×D4 | semidirect |
| 72. D4×C251 | C2×D4 | semidirect |
| 96. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 104. C251 | #3038 | semidirect |
| 108. C4×#41 | D251 | semidirect |
| 123. C4×Q8 | C2×D251 | semidirect |
| 125. C4×D4 | C2×D251 | semidirect |
| 134. #41 | D1004 | semidirect |
| 168. Q8 | C2×D1004 | semidirect |
| 176. D4 | C2×D1004 | semidirect |
| 201. C4 | #22548740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×#22548712 | 2 |
| #30631887 | 2 |
| #30631882 | 2 |
| #30631711 | 2 |
| #30631691 | 2 |
| C4×#41×C251 | 2 |
| #3038 | 251 |