Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31800376 | C2 | semidirect |
| 3. D4×#14555660 | C2 | semidirect |
| 4. #31799752 | C2 | semidirect |
| 5. #31799748 | C2 | semidirect |
| 6. #31799745 | C2 | semidirect |
| 7. #474×C277 | C2 | semidirect |
| 52. #14555660 | D8 | semidirect |
| 57. D4×C277 | SD16 | semidirect |
| 85. C277 | #1665 | semidirect |
| 88. #474 | D277 | semidirect |
| 139. D4 | #17984550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800376 | 2 |
| #31800197 | 2 |
| D4×#14555660 | 2 |
| #31799752 | 2 |
| #31799748 | 2 |
| #31799745 | 2 |
| #474×C277 | 2 |
| #1665 | 277 |