Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22576148 | C2 | semidirect |
| 3. C2×#22576139 | C2 | semidirect |
| 4. #31773815 | C2 | semidirect |
| 5. #31773799 | C2 | semidirect |
| 6. #31773752 | C2 | semidirect |
| 7. C4×C22⋊C4×C271 | C2 | semidirect |
| 9. C22×Dic542 | C22 | semidirect |
| 16. C2×C4⋊Dic271 | C22 | semidirect |
| 17. C2×Dic271⋊C4 | C22 | semidirect |
| 19. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 23. C2×C42×C271 | C22 | semidirect |
| 24. #95×C271 | C22 | semidirect |
| 85. C22×C271 | #124 | semidirect |
| 107. C271 | #2435 | semidirect |
| 115. C4×C22⋊C4 | D271 | semidirect |
| 131. C2×C42 | C2×D271 | semidirect |
| 132. #95 | C2×D271 | semidirect |
| 199. C22 | #22576148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1084 | 2 |
| C2×#22576148 | 2 |
| C2×#22576139 | 2 |
| #31773815 | 2 |
| #31773799 | 2 |
| #31773752 | 2 |
| C4×C22⋊C4×C271 | 2 |
| #2435 | 271 |