Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31774273 | C2 | semidirect |
| 2. #31774092 | C2 | semidirect |
| 3. #31773975 | C2 | semidirect |
| 4. #31773647 | C2 | semidirect |
| 5. #31773641 | C2 | semidirect |
| 6. #31773640 | C2 | semidirect |
| 7. #459×C271 | C2 | semidirect |
| 53. C271⋊C8 | D8 | semidirect |
| 92. C271 | #1687 | semidirect |
| 96. #459 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774273 | 2 |
| #31774092 | 2 |
| #31773975 | 2 |
| #31773647 | 2 |
| #31773641 | 2 |
| #31773640 | 2 |
| #459×C271 | 2 |
| #1687 | 271 |