Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic542 | C2 | semidirect |
| 3. #31774244 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31774187 | C2 | semidirect |
| 6. #31774186 | C2 | semidirect |
| 7. #31774097 | C2 | semidirect |
| 8. #31774095 | C2 | semidirect |
| 9. C8×Dic542 | C2 | semidirect |
| 10. #31773982 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 77. Dic542 | SD16 | semidirect |
| 91. Q8×C271 | #41 | semidirect |
| 125. C271 | #3362 | semidirect |
| 137. C4×SD16 | D271 | semidirect |
| 206. Q8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic542 | 2 |
| #31774568 | 2 |
| #31774244 | 2 |
| #31774242 | 2 |
| #31774187 | 2 |
| #31774186 | 2 |
| #31774097 | 2 |
| #31774095 | 2 |
| C8×Dic542 | 2 |
| #31773982 | 2 |
| C4×SD16×C271 | 2 |
| #3362 | 271 |