Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774207 | C2 | semidirect |
| 4. #31774196 | C2 | semidirect |
| 5. #31774191 | C2 | semidirect |
| 6. #31774176 | C2 | semidirect |
| 7. C2×#22576093 | C2 | semidirect |
| 8. #31773925 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 42. #16864654 | Q8 | semidirect |
| 123. C271 | #3083 | semidirect |
| 131. #428 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774378 | 2 |
| #31774207 | 2 |
| #31774196 | 2 |
| #31774191 | 2 |
| #31774176 | 2 |
| C2×#22576093 | 2 |
| #31773925 | 2 |
| #31773899 | 2 |
| #31773891 | 2 |
| #428×C271 | 2 |
| #3083 | 271 |