Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1088 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D271 |
| commutator, socle, cosocle | C23×C271 | C24 |
| Fitting | #390×C271 | C2 |
| prime radical | C22×D4×D271 | C2 |
| hypercenter | #390 | D271 |
| hypocenter | C271 | #2435 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#22576148 | C2 | semidirect |
| 3. C2×#22576147 | C2 | semidirect |
| 4. C2×#22576140 | C2 | semidirect |
| 5. #31773813 | C2 | semidirect |
| 6. #31773798 | C2 | semidirect |
| 7. #31773752 | C2 | semidirect |
| 8. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 9. #390×C271 | C2 | semidirect |
| 11. C22×Dic542 | C22 | semidirect |
| 21. C2×C4⋊Dic271 | C22 | semidirect |
| 22. C2×C22⋊Dic271 | C22 | semidirect |
| 25. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 27. C2×C4×Dic271 | C22 | semidirect |
| 28. C271⋊#95 | C22 | semidirect |
| 30. C2×C4⋊C4×C271 | C22 | semidirect |
| 31. C2×C22⋊C4×C271 | C22 | semidirect |
| 32. C2×C42×C271 | C22 | semidirect |
| 136. C2×D271 | #124 | semidirect |
| 151. C271 | #2435 | semidirect |
| 159. #390 | D271 | semidirect |
| 175. C2×C4⋊C4 | C2×D271 | semidirect |
| 181. C2×C22⋊C4 | C2×D271 | semidirect |
| 183. C2×C42 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D271 | 2 |
| C2×#22576148 | 2 |
| C2×#22576147 | 2 |
| C2×#22576140 | 2 |
| #31773813 | 2 |
| #31773798 | 2 |
| #31773752 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| #390×C271 | 2 |
| #2435 | 271 |