Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774528 | C2 | semidirect |
| 3. #31774202 | C2 | semidirect |
| 4. #31774199 | C2 | semidirect |
| 5. #31774190 | C2 | semidirect |
| 6. #31774175 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. C2×#22576093 | C2 | semidirect |
| 9. #31773925 | C2 | semidirect |
| 64. #41×C271 | Q8 | semidirect |
| 123. C271 | #3083 | semidirect |
| 166. #41 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774528 | 2 |
| #31774380 | 2 |
| #31774202 | 2 |
| #31774199 | 2 |
| #31774190 | 2 |
| #31774175 | 2 |
| #31773939 | 2 |
| C2×#22576093 | 2 |
| #31773925 | 2 |
| #31773893 | 2 |
| #417×C271 | 2 |
| #3083 | 271 |