Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #31800405 | C2 | semidirect |
| 3. #31800209 | C2 | semidirect |
| 4. #31799747 | C2 | semidirect |
| 5. #31799732 | C2 | semidirect |
| 65. D4×C277 | Q16 | semidirect |
| 92. C277 | #1649 | semidirect |
| 152. D4 | #17984553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic554 | 2 |
| #31800405 | 2 |
| #31800209 | 2 |
| #31799747 | 2 |
| #31799732 | 2 |
| D4⋊#14555660 | 2 |
| #474×C277 | 2 |
| #1649 | 277 |