Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774625 | C2 | semidirect |
| 2. #31774261 | C2 | semidirect |
| 3. #31774243 | C2 | semidirect |
| 4. #31774197 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774094 | C2 | semidirect |
| 8. #31774028 | C2 | semidirect |
| 9. #31773997 | C2 | semidirect |
| 10. C4×#16864642 | C2 | semidirect |
| 76. Dic542 | #41 | semidirect |
| 124. C271 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774625 | 2 |
| #31774261 | 2 |
| #31774243 | 2 |
| #31774197 | 2 |
| #31774177 | 2 |
| #31774094 | 2 |
| #31774028 | 2 |
| #31773997 | 2 |
| C4×#16864642 | 2 |
| #550×C271 | 2 |
| #3368 | 271 |