Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic542 | C2 | semidirect |
| 3. #31774248 | C2 | semidirect |
| 4. #31774228 | C2 | semidirect |
| 5. #31774183 | C2 | semidirect |
| 6. #31774126 | C2 | semidirect |
| 7. #31774103 | C2 | semidirect |
| 8. #31774038 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. C2×#22576085 | C2 | semidirect |
| 11. C8×D4×C271 | C2 | semidirect |
| 83. Dic542 | #41 | semidirect |
| 96. D4×C271 | SD16 | semidirect |
| 128. C271 | #3298 | semidirect |
| 139. C8×D4 | D271 | semidirect |
| 217. D4 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic542 | 2 |
| #31774551 | 2 |
| #31774248 | 2 |
| #31774228 | 2 |
| #31774183 | 2 |
| #31774126 | 2 |
| #31774103 | 2 |
| #31774038 | 2 |
| C4×#16864643 | 2 |
| C2×#22576085 | 2 |
| C8×D4×C271 | 2 |
| #3298 | 271 |