Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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. #31774297 | C2 | semidirect |
| 3. #31773721 | C2 | semidirect |
| 4. #31773717 | C2 | semidirect |
| 7. #365×C271 | C2 | semidirect |
| 59. C271 | #2231 | semidirect |
| 64. #365 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774297 | 2 |
| #31774013 | 2 |
| #31773721 | 2 |
| #31773717 | 2 |
| #31773708 | 2 |
| #31773706 | 2 |
| #365×C271 | 2 |
| #2231 | 271 |