Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#17984546 | C2 | semidirect |
| 3. C2×#22579801 | C2 | semidirect |
| 4. #31799859 | C2 | semidirect |
| 5. #31799765 | C2 | semidirect |
| 6. #31799764 | C2 | semidirect |
| 7. C2×#102×C277 | C2 | semidirect |
| 15. #22579851 | C4 | semidirect |
| 42. C2×#14555660 | D4 | semidirect |
| 60. C2×C8×C277 | D4 | semidirect |
| 145. C277 | #1895 | semidirect |
| 150. C2×#102 | D277 | semidirect |
| 200. C2×C8 | C22⋊D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17984546 | 2 |
| C2×#22579851 | 2 |
| C2×#22579801 | 2 |
| #31799859 | 2 |
| #31799765 | 2 |
| #31799764 | 2 |
| C2×#102×C277 | 2 |
| #1895 | 277 |