Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. #31774273 | C2 | semidirect |
| 4. #31774131 | C2 | semidirect |
| 5. #31774097 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774042 | C2 | semidirect |
| 8. #31774040 | C2 | semidirect |
| 9. C4×#16864644 | C2 | semidirect |
| 10. D4×C271⋊C8 | C2 | semidirect |
| 11. #550×C271 | C2 | semidirect |
| 51. #16864644 | D4 | semidirect |
| 131. C4×C271 | #135 | semidirect |
| 142. C271 | #3287 | semidirect |
| 146. #550 | D271 | semidirect |
| 276. 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 |
| #31774273 | 2 |
| #31774131 | 2 |
| #31774097 | 2 |
| #31774094 | 2 |
| #31774042 | 2 |
| #31774040 | 2 |
| C4×#16864644 | 2 |
| D4×C271⋊C8 | 2 |
| #550×C271 | 2 |
| #3287 | 271 |