Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31774374 | C2 | semidirect |
| 4. C2×#22576078 | C2 | semidirect |
| 5. #31773654 | C2 | semidirect |
| 6. #31773653 | C2 | semidirect |
| 10. #22576158 | C4 | semidirect |
| 11. #22576147 | C4 | semidirect |
| 109. C271 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774468 | 2 |
| #31774374 | 2 |
| #31773914 | 2 |
| C2×#22576078 | 2 |
| #31773654 | 2 |
| #31773653 | 2 |
| #421×C271 | 2 |
| #1912 | 271 |