Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#22548648 | C2 | semidirect |
| 4. #30631450 | C2 | semidirect |
| 5. #340×C251 | C2 | semidirect |
| 9. C2×C8×D251 | C4 | semidirect |
| 48. C251⋊C8 | C22⋊C4 | semidirect |
| 67. C2×D251 | #107 | semidirect |
| 80. C251 | #1808 | semidirect |
| 86. #340 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×#22548648 | 2 |
| #30631544 | 2 |
| #30631450 | 2 |
| #340×C251 | 2 |
| #1808 | 251 |