Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #31800019 | C2 | semidirect |
| 3. #31800008 | C2 | semidirect |
| 4. #31800006 | C2 | semidirect |
| 5. #31799984 | C2 | semidirect |
| 6. #31799975 | C2 | semidirect |
| 7. #421×C277 | C2 | semidirect |
| 12. C2×#17984564 | C4 | semidirect |
| 18. C2×D4×D277 | C4 | semidirect |
| 19. C2×#17984547 | C22 | semidirect |
| 20. #22579839 | C22 | semidirect |
| 28. C2×M16×C277 | C22 | semidirect |
| 29. #117×C277 | C22 | semidirect |
| 153. C277 | #1795 | semidirect |
| 157. #421 | D277 | semidirect |
| 175. C2×M16 | C2×D277 | semidirect |
| 177. #117 | C2×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579926 | 2 |
| #31800019 | 2 |
| #31800008 | 2 |
| #31800006 | 2 |
| #31799984 | 2 |
| #31799975 | 2 |
| #421×C277 | 2 |
| #1795 | 277 |