Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22579816 | C2 | semidirect |
| 3. #31800010 | C2 | semidirect |
| 5. C2×#22579798 | C2 | semidirect |
| 7. #405×C277 | C2 | semidirect |
| 13. C2×#17984552 | C4 | semidirect |
| 106. C277 | #1977 | semidirect |
| 114. #405 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17984552 | 2 |
| C2×#22579816 | 2 |
| #31800010 | 2 |
| #31800006 | 2 |
| C2×#22579798 | 2 |
| C2×#22579796 | 2 |
| #405×C277 | 2 |
| #1977 | 277 |