Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #392×C271 | C2 |
| hypercenter | #392 | D271 |
| hypocenter | C271 | #2388 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#16864653 | C2 | semidirect |
| 2. C2×D4×Dic271 | C2 | semidirect |
| 3. C2×(C22⋊D271)⋊C4 | C2 | semidirect |
| 4. #31773818 | C2 | semidirect |
| 5. #31773813 | C2 | semidirect |
| 6. #31773811 | C2 | semidirect |
| 7. #31773809 | C2 | semidirect |
| 8. #31773805 | C2 | semidirect |
| 9. C22⋊C4×Dic271 | C2 | semidirect |
| 10. #31773744 | C2 | semidirect |
| 11. #392×C271 | C2 | semidirect |
| 53. C22×Dic271 | D4 | semidirect |
| 60. C2×C4×D271 | D4 | semidirect |
| 104. C2×Dic271 | #41 | semidirect |
| 117. C23×C271 | #41 | semidirect |
| 127. C2×C4×C271 | #41 | semidirect |
| 166. C271 | #2388 | semidirect |
| 176. #392 | D271 | semidirect |
| 265. C23 | #16864653 | semidirect |
| 294. C2×C4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864653 | 2 |
| C2×D4×Dic271 | 2 |
| C2×(C22⋊D271)⋊C4 | 2 |
| #31773818 | 2 |
| #31773813 | 2 |
| #31773811 | 2 |
| #31773809 | 2 |
| #31773805 | 2 |
| C22⋊C4×Dic271 | 2 |
| #31773744 | 2 |
| #392×C271 | 2 |
| #2388 | 271 |