Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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. #31800435 | C2 | semidirect |
| 2. D16×D277 | C2 | semidirect |
| 3. #31799839 | C2 | semidirect |
| 4. D8864 | C2 | semidirect |
| 5. #31799837 | C2 | semidirect |
| 6. #31799835 | C2 | semidirect |
| 7. SD64×C277 | C2 | semidirect |
| 12. D4432 | C22 | semidirect |
| 15. #22579786 | C22 | semidirect |
| 16. Q32×C277 | C22 | semidirect |
| 18. C32×C277 | C22 | semidirect |
| 54. C277 | #2263 | semidirect |
| 59. SD64 | D277 | semidirect |
| 65. Q32 | C2×D277 | semidirect |
| 73. C32 | C2×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800435 | 2 |
| D16×D277 | 2 |
| #31799839 | 2 |
| D8864 | 2 |
| #31799837 | 2 |
| #31799835 | 2 |
| SD64×C277 | 2 |
| #2263 | 277 |