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. #31800374 | C2 | semidirect |
| 2. #31800282 | C2 | semidirect |
| 3. D4×#14555660 | C2 | semidirect |
| 4. #31799752 | C2 | semidirect |
| 5. #31799747 | C2 | semidirect |
| 6. #31799746 | C2 | semidirect |
| 49. #14555660 | D8 | semidirect |
| 58. D4×C277 | SD16 | semidirect |
| 85. C277 | #1665 | semidirect |
| 139. D4 | #17984551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800374 | 2 |
| #31800282 | 2 |
| D4×#14555660 | 2 |
| #31799752 | 2 |
| #31799747 | 2 |
| #31799746 | 2 |
| #459×C277 | 2 |
| #1665 | 277 |