Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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 | #394×C271 | C2 |
| prime radical | C22×D4×C271 | C22 |
| hypercenter | #394 | D271 |
| hypocenter | C271 | #2398 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22576125 | C2 | semidirect |
| 3. #31773837 | C2 | semidirect |
| 4. #31773836 | C2 | semidirect |
| 5. #31773825 | C2 | semidirect |
| 7. #31773809 | C2 | semidirect |
| 8. C22⋊C4×Dic271 | C2 | semidirect |
| 9. C22⋊C4×Dic271 | C2 | semidirect |
| 10. #31773742 | C2 | semidirect |
| 134. C271 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576125 | 2 |
| C2×D4×Dic271 | 2 |
| #31773837 | 2 |
| #31773836 | 2 |
| #31773825 | 2 |
| #31773811 | 2 |
| #31773809 | 2 |
| C22⋊C4×Dic271 | 2 |
| #31773742 | 2 |
| #394×C271 | 2 |
| #2398 | 271 |