Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31773945 | C2 | semidirect |
| 2. #31773923 | C2 | semidirect |
| 6. #31773653 | C2 | semidirect |
| 7. #424×C271 | C2 | semidirect |
| 89. C271 | #2098 | semidirect |
| 93. #424 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773945 | 2 |
| #31773923 | 2 |
| #31773915 | 2 |
| #31773913 | 2 |
| #31773863 | 2 |
| #31773653 | 2 |
| #424×C271 | 2 |
| #2098 | 271 |