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. #31774525 | C2 | semidirect |
| 3. #31774205 | C2 | semidirect |
| 4. #31774198 | C2 | semidirect |
| 5. #31774193 | C2 | semidirect |
| 6. #31774178 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. C2×#22576094 | C2 | semidirect |
| 11. #424×C271 | C2 | semidirect |
| 42. #16864654 | Q8 | semidirect |
| 123. C271 | #3083 | semidirect |
| 133. #424 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774377 | 2 |
| #31774205 | 2 |
| #31774198 | 2 |
| #31774193 | 2 |
| #31774178 | 2 |
| #31773939 | 2 |
| C2×#22576094 | 2 |
| #31773899 | 2 |
| #31773894 | 2 |
| #424×C271 | 2 |
| #3083 | 271 |