Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#22579807 | C2 | semidirect |
| 3. C2×#22579806 | C2 | semidirect |
| 4. #31800001 | C2 | semidirect |
| 5. C2×#22579798 | C2 | semidirect |
| 6. #31799907 | C2 | semidirect |
| 7. #417×C277 | C2 | semidirect |
| 11. #22579927 | C4 | semidirect |
| 154. C277 | #1793 | semidirect |
| 160. #417 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579927 | 2 |
| C2×#22579807 | 2 |
| C2×#22579806 | 2 |
| #31800001 | 2 |
| C2×#22579798 | 2 |
| #31799907 | 2 |
| #417×C277 | 2 |
| #1793 | 277 |