Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22576180 | C2 | semidirect |
| 2. #31774568 | C2 | semidirect |
| 3. #31774271 | C2 | semidirect |
| 4. #31774128 | C2 | semidirect |
| 5. #31774104 | C2 | semidirect |
| 6. #31774092 | C2 | semidirect |
| 7. #31774057 | C2 | semidirect |
| 8. #31774042 | C2 | semidirect |
| 9. C4×#16864642 | C2 | semidirect |
| 10. D4×C271⋊C8 | C2 | semidirect |
| 11. #547×C271 | C2 | semidirect |
| 52. #16864642 | D4 | semidirect |
| 129. C4×C271 | #135 | semidirect |
| 140. C271 | #3284 | semidirect |
| 144. #547 | D271 | semidirect |
| 272. C4 | #22576180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| #31774568 | 2 |
| #31774271 | 2 |
| #31774128 | 2 |
| #31774104 | 2 |
| #31774092 | 2 |
| #31774057 | 2 |
| #31774042 | 2 |
| C4×#16864642 | 2 |
| D4×C271⋊C8 | 2 |
| #547×C271 | 2 |
| #3284 | 271 |