Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31800768 | C2 | semidirect |
| 3. #31800008 | C2 | semidirect |
| 4. #31800006 | C2 | semidirect |
| 5. #31799975 | C2 | semidirect |
| 6. #31799758 | C2 | semidirect |
| 7. H(3,ℤ/4)×C277 | C2 | semidirect |
| 14. #22579877 | C4 | semidirect |
| 15. #22579868 | C4 | semidirect |
| 44. C2×#14555660 | D4 | semidirect |
| 53. C2×C8×C277 | D4 | semidirect |
| 115. C277 | #1910 | semidirect |
| 123. H(3,ℤ/4) | D277 | semidirect |
| 165. C2×C8 | D1108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800768 | 2 |
| #31800571 | 2 |
| #31800008 | 2 |
| #31800006 | 2 |
| #31799975 | 2 |
| #31799758 | 2 |
| H(3,ℤ/4)×C277 | 2 |
| #1910 | 277 |