Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #31799893 | C2 | semidirect |
| 3. #31799891 | C2 | semidirect |
| 4. #31799860 | C2 | semidirect |
| 6. C4×C22⋊Dic277 | C2 | semidirect |
| 7. C4×C22⋊C4×C277 | C2 | semidirect |
| 10. C2×#17984542 | C22 | semidirect |
| 12. C2×#17984540 | C4 | semidirect |
| 17. C2×C4×Dic277 | C22 | semidirect |
| 18. #22579787 | C22 | semidirect |
| 19. #22579787 | C22 | semidirect |
| 22. C2×C42×C277 | C22 | semidirect |
| 23. #95×C277 | C22 | semidirect |
| 99. C277 | #2312 | semidirect |
| 107. C4×C22⋊C4 | D277 | semidirect |
| 120. C2×C42 | C2×D277 | semidirect |
| 123. #95 | C2×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17984540 | 2 |
| #31799893 | 2 |
| #31799891 | 2 |
| #31799860 | 2 |
| #31799857 | 2 |
| C4×C22⋊Dic277 | 2 |
| C4×C22⋊C4×C277 | 2 |
| #2312 | 277 |