Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31799906 | C2 | semidirect |
| 3. #31799893 | C2 | semidirect |
| 4. #31799891 | C2 | semidirect |
| 6. C4×#17984540 | C2 | semidirect |
| 7. #31799849 | C2 | semidirect |
| 8. #31799848 | C2 | semidirect |
| 9. #376×C277 | C2 | semidirect |
| 13. #22579868 | C4 | semidirect |
| 35. C2×Dic554 | C2×C4 | semidirect |
| 49. #17984540 | C2×C4 | semidirect |
| 50. #17984540 | C2×C4 | semidirect |
| 59. C42×C277 | C2×C4 | semidirect |
| 119. C277 | #2372 | semidirect |
| 129. #376 | D277 | semidirect |
| 179. C42 | C4×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579868 | 2 |
| #31799906 | 2 |
| #31799893 | 2 |
| #31799891 | 2 |
| #31799880 | 2 |
| C4×#17984540 | 2 |
| #31799849 | 2 |
| #31799848 | 2 |
| #376×C277 | 2 |
| #2372 | 277 |