Finite Group DatabasebetaFinite Group DatabasebetaOrder 8112.
138 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C132 | C42 |
| prime radical, cosocle | C3×D132 | C22 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C3⋊#10621730 | C4 | semidirect |
| 6. C3⋊#10621729 | C4 | semidirect |
| 7. C3⋊#10621728 | C4 | semidirect |
| 8. C13×C3⋊#261 | C4 | semidirect |
| 10. C3×#10621730 | C4 | semidirect |
| 11. C3×C13×#261 | C4 | semidirect |
| 20. #10621730 | Dic3 | semidirect |
| 24. C13×#261 | Dic3 | semidirect |
| 27. C3×C132 | C42 | semidirect |
| 39. C132 | C4×Dic3 | semidirect |
| 48. C3⋊#261 | #261 | direct (N × H) |
| 50. C3×#261 | #261 | semidirect |
| 78. #261 | C3⋊#261 | direct (N × H) |
| 85. C3×C13 | C4×#261 | semidirect |
| 86. C3×C13 | C4×#261 | semidirect |
| 99. C13 | Dic3×#261 | semidirect |
| 100. C13 | C4×C3⋊#261 | semidirect |
| 121. C3 | #2612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×C3⋊#261 | 2 |
| C3×D13×#261 | 2 |
| #72220646 | 2 |
| #2612 | 3 |
| C4×C3⋊#261 | 13 |
| Dic3×#261 | 13 |