Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #31800378 | C2 | semidirect |
| 2. #31800378 | C2 | semidirect |
| 3. #31800374 | C2 | semidirect |
| 4. #31800349 | C2 | semidirect |
| 5. #31800348 | C2 | semidirect |
| 6. #31799724 | C2 | semidirect |
| 7. #493×C277 | C2 | semidirect |
| 48. #14555660 | D8 | semidirect |
| 81. C277 | #1721 | semidirect |
| 85. #493 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800378 | 2 |
| #31800374 | 2 |
| #31800349 | 2 |
| #31800348 | 2 |
| #31799724 | 2 |
| #493×C277 | 2 |
| #1721 | 277 |