Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31774622 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774245 | C2 | semidirect |
| 5. #31774200 | C2 | semidirect |
| 6. #31774098 | C2 | semidirect |
| 7. #31774096 | C2 | semidirect |
| 8. #31774024 | C2 | semidirect |
| 9. #31773996 | C2 | semidirect |
| 10. C4×#16864642 | C2 | semidirect |
| 11. #474×C271 | C2 | semidirect |
| 77. Dic542 | #41 | semidirect |
| 124. C271 | #3368 | semidirect |
| 131. #474 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774622 | 2 |
| #31774568 | 2 |
| #31774260 | 2 |
| #31774245 | 2 |
| #31774200 | 2 |
| #31774098 | 2 |
| #31774096 | 2 |
| #31774024 | 2 |
| #31773996 | 2 |
| C4×#16864642 | 2 |
| #474×C271 | 2 |
| #3368 | 271 |