Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31800819 | C2 | semidirect |
| 2. #31800438 | C2 | semidirect |
| 3. C2×#22579824 | C2 | semidirect |
| 4. #31799817 | C2 | semidirect |
| 5. #31799808 | C2 | semidirect |
| 6. #31799786 | C2 | semidirect |
| 7. #472×C277 | C2 | semidirect |
| 90. C277 | #2193 | semidirect |
| 95. #472 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800819 | 2 |
| #31800438 | 2 |
| C2×#22579824 | 2 |
| #31799817 | 2 |
| #31799808 | 2 |
| #31799786 | 2 |
| #472×C277 | 2 |
| #2193 | 277 |