Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 4. #31774248 | C2 | semidirect |
| 6. #31774183 | C2 | semidirect |
| 8. #31774108 | C2 | semidirect |
| 9. #31774005 | C2 | semidirect |
| 11. #446×C271 | C2 | semidirect |
| 116. C271 | #3369 | semidirect |
| 126. #446 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic542 | 2 |
| #31774620 | 2 |
| #31774257 | 2 |
| #31774248 | 2 |
| #31774188 | 2 |
| #31774183 | 2 |
| #31774120 | 2 |
| #31774108 | 2 |
| #31774005 | 2 |
| C4×#16864643 | 2 |
| #446×C271 | 2 |
| #3369 | 271 |