Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31800407 | C2 | semidirect |
| 2. #31800400 | C2 | semidirect |
| 5. #31800353 | C2 | semidirect |
| 7. #322×C277 | C2 | semidirect |
| 54. C8×C277 | SD16 | semidirect |
| 69. C277 | #1714 | semidirect |
| 77. #322 | D277 | semidirect |
| 124. C8 | #17984552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800407 | 2 |
| #31800400 | 2 |
| #31800375 | 2 |
| #31800353 | 2 |
| #31800349 | 2 |
| #322×C277 | 2 |
| #1714 | 277 |