Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31800375 | C2 | semidirect |
| 3. #31800297 | C2 | semidirect |
| 4. #31800293 | C2 | semidirect |
| 5. #31799745 | C2 | semidirect |
| 6. #31799731 | C2 | semidirect |
| 7. Q8⋊C8×C277 | C2 | semidirect |
| 69. Q8×C277 | SD16 | semidirect |
| 98. C277 | #1631 | semidirect |
| 105. Q8⋊C8 | D277 | semidirect |
| 153. Q8 | #17984552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800674 | 2 |
| #31800375 | 2 |
| #31800297 | 2 |
| #31800293 | 2 |
| #31799745 | 2 |
| #31799731 | 2 |
| Q8⋊C8×C277 | 2 |
| #1631 | 277 |