Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊#6923 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | C25×C61 | C4 |
| socle | C23×C61 | C22⋊C4 |
| hypercenter | C25 | #6923 |
| hypocenter | C61 | C22×#99 |
| LCS | G ▷ C22×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C24 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊#6923 | C2 | semidirect |
| 2. C2×#14519835 | C2 | direct (N × H) |
| 6. C2×C22⋊#6923 | C22 | semidirect |
| 7. #14519835 | C22 | direct (N × H) |
| 11. C22×C22⋊D61 | C4 | semidirect |
| 13. C23×Dic61 | C4 | semidirect |
| 14. C25×C61 | C4 | semidirect |
| 19. C24×C61 | C2×C4 | semidirect |
| 31. C2×C22⋊D61 | C2×C4 | semidirect |
| 35. C22×Dic61 | C2×C4 | semidirect |
| 37. C22⋊#6923 | C23 | semidirect |
| 47. C23×C61 | C22×C4 | semidirect |
| 64. C2×Dic61 | C22×C4 | semidirect |
| 71. C22×C61 | #99 | semidirect |
| 89. C2×C61 | C2×#99 | semidirect |
| 96. C61 | C22×#99 | semidirect |
| 98. C25 | #6923 | semidirect |
| 117. C24 | C2×#6923 | semidirect |
| 150. C23 | C22×#6923 | semidirect |
| 172. C22 | #14519835 | direct (N × H) |
| 183. C2 | C2×#14519835 | direct (N × H) |