Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 1. #31800133 | C2 | semidirect |
| 4. #31799752 | C2 | semidirect |
| 6. C8×#14555660 | C2 | semidirect |
| 7. Q8⋊C8×C277 | C2 | semidirect |
| 50. #14555660 | M16 | semidirect |
| 51. #14555660 | SD16 | semidirect |
| 77. C277 | #1590 | semidirect |
| 83. Q8⋊C8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800133 | 2 |
| C4×#17984550 | 2 |
| #31800079 | 2 |
| #31799752 | 2 |
| #31799731 | 2 |
| C8×#14555660 | 2 |
| Q8⋊C8×C277 | 2 |
| #1590 | 277 |