Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
180 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31800080 | C2 | semidirect |
| 3. #31800079 | C2 | semidirect |
| 4. #31799754 | C2 | semidirect |
| 5. #31799731 | C2 | semidirect |
| 6. C8×#14555660 | C2 | semidirect |
| 7. D4⋊C8×C277 | C2 | semidirect |
| 51. #14555660 | M16 | semidirect |
| 52. #14555660 | D8 | semidirect |
| 83. C277 | #1589 | semidirect |
| 90. D4⋊C8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17984548 | 2 |
| #31800080 | 2 |
| #31800079 | 2 |
| #31799754 | 2 |
| #31799731 | 2 |
| C8×#14555660 | 2 |
| D4⋊C8×C277 | 2 |
| #1589 | 277 |