Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #31774305 | C2 | semidirect |
| 4. #31774304 | C2 | semidirect |
| 5. #31774299 | C2 | semidirect |
| 6. #31774296 | C2 | semidirect |
| 7. #31774296 | C2 | semidirect |
| 11. #499×C271 | C2 | semidirect |
| 43. #16864637 | Q8 | semidirect |
| 44. #16864637 | Q8 | semidirect |
| 99. C271 | #3166 | semidirect |
| 108. #499 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774453 | 2 |
| #125×D271 | 2 |
| #31774305 | 2 |
| #31774304 | 2 |
| #31774299 | 2 |
| #31774296 | 2 |
| #31773938 | 2 |
| #31773936 | 2 |
| C4×#16864637 | 2 |
| #499×C271 | 2 |
| #3166 | 271 |