Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#22576125 | C2 | semidirect |
| 3. #31774232 | C2 | semidirect |
| 4. #31774207 | C2 | semidirect |
| 5. #31774118 | C2 | semidirect |
| 6. #31774055 | C2 | semidirect |
| 8. #31774003 | C2 | semidirect |
| 9. #31773994 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 131. C271 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774428 | 2 |
| C2×#22576125 | 2 |
| #31774232 | 2 |
| #31774207 | 2 |
| #31774118 | 2 |
| #31774055 | 2 |
| #31774035 | 2 |
| #31774003 | 2 |
| #31773994 | 2 |
| #31773951 | 2 |
| #481×C271 | 2 |
| #3117 | 271 |