Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#22579903 | C2 | semidirect |
| 2. C2×#22579823 | C2 | semidirect |
| 3. C2×D4432 | C2 | semidirect |
| 4. #31800239 | C2 | semidirect |
| 5. #31799802 | C2 | semidirect |
| 6. #31799781 | C2 | semidirect |
| 7. #358×C277 | C2 | semidirect |
| 35. D2216 | D4 | semidirect |
| 43. Q16×C277 | D4 | semidirect |
| 89. C277 | #2186 | semidirect |
| 95. #358 | D277 | semidirect |
| 123. Q16 | D1108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579903 | 2 |
| C2×#22579823 | 2 |
| C2×D4432 | 2 |
| #31800239 | 2 |
| #31799802 | 2 |
| #31799781 | 2 |
| #358×C277 | 2 |
| #2186 | 277 |