Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31773933 | C2 | semidirect |
| 3. #31773915 | C2 | semidirect |
| 4. #31773914 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #31773853 | C2 | semidirect |
| 7. #410×C271 | C2 | semidirect |
| 13. C2×#16864644 | C4 | semidirect |
| 14. C2×#16864642 | C4 | semidirect |
| 15. C2×#16864641 | C4 | semidirect |
| 16. C2×#16864639 | C4 | semidirect |
| 132. C271 | #1976 | semidirect |
| 139. #410 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| #31773933 | 2 |
| #31773915 | 2 |
| #31773914 | 2 |
| #31773870 | 2 |
| #31773853 | 2 |
| #410×C271 | 2 |
| #1976 | 271 |