Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 812 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 |
|---|---|---|
| 1. C22×#16860797 | C2 | semidirect |
| 2. C22×#16860795 | C2 | semidirect |
| 3. C2×#22548689 | C2 | semidirect |
| 4. #30631832 | C2 | direct (N × H) |
| 5. C2×#22548639 | C2 | semidirect |
| 6. C2×#22548636 | C2 | semidirect |
| 7. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 8. C22×#41×C251 | C2 | semidirect |
| 12. C2×#16860797 | C22 | semidirect |
| 14. C2×#16860795 | C22 | semidirect |
| 18. #22548689 | C22 | semidirect |
| 21. #22548639 | C22 | semidirect |
| 22. #22548636 | C22 | semidirect |
| 23. C22⋊(C251⋊C8) | C22 | semidirect |
| 27. C2×#41×C251 | C22 | semidirect |
| 57. C2×Q8×C251 | D4 | semidirect |
| 63. C2×D4×C251 | D4 | semidirect |
| 97. Q8×C251 | C2×D4 | semidirect |
| 101. D4×C251 | C2×D4 | semidirect |
| 138. C2×C251 | #449 | semidirect |
| 143. C251 | C2×#449 | semidirect |
| 145. C22×#41 | D251 | semidirect |
| 156. C2×#41 | C2×D251 | semidirect |
| 185. C2×Q8 | C22⋊D251 | semidirect |
| 197. C2×D4 | C22⋊D251 | semidirect |
| 233. Q8 | C2×C22⋊D251 | semidirect |
| 241. D4 | C2×C22⋊D251 | semidirect |
| 283. C2 | #30631832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C22×#16860795 | 2 |
| C2×#22548689 | 2 |
| #30631832 | 2 |
| C2×#22548639 | 2 |
| C2×#22548636 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C22×#41×C251 | 2 |
| C2×#449 | 251 |