Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #30632488 | C2 | semidirect |
| 2. #30631954 | C2 | semidirect |
| 3. #30631854 | C2 | semidirect |
| 4. #30631805 | C2 | semidirect |
| 5. #493×C251 | C2 | semidirect |
| 6. #22548760 | C22 | semidirect |
| 7. #22548741 | C22 | semidirect |
| 12. #22548721 | C22 | semidirect |
| 13. #22548651 | C22 | semidirect |
| 14. #22548643 | C22 | semidirect |
| 15. #22548632 | C22 | semidirect |
| 16. C2×D8×C251 | C22 | semidirect |
| 17. #127×C251 | C22 | semidirect |
| 18. C4×C8×C251 | C22 | semidirect |
| 23. Dic1004 | D4 | semidirect |
| 24. #16860799 | D4 | semidirect |
| 26. D2008 | D4 | semidirect |
| 64. C251 | #3292 | semidirect |
| 67. #493 | D251 | semidirect |
| 77. C2×D8 | C2×D251 | semidirect |
| 79. #127 | C2×D251 | semidirect |
| 83. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632488 | 2 |
| #30631954 | 2 |
| #30631854 | 2 |
| #30631805 | 2 |
| #493×C251 | 2 |
| #3292 | 251 |