Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #31800348 | C2 | semidirect |
| 2. #31800207 | C2 | semidirect |
| 3. D4×#14555660 | C2 | semidirect |
| 4. #31799754 | C2 | semidirect |
| 5. #31799749 | C2 | semidirect |
| 6. #31799746 | C2 | semidirect |
| 84. C277 | #1681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800348 | 2 |
| #31800207 | 2 |
| D4×#14555660 | 2 |
| #31799754 | 2 |
| #31799749 | 2 |
| #31799746 | 2 |
| #459×C277 | 2 |
| #1681 | 277 |