Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
436 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C22⋊C8×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | C22⋊C8 | #6923 |
| hypocenter | C61 | C4×C22⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C8×#6923 | C2 | semidirect |
| 4. (C2×#6923)⋊C8 | C2 | semidirect |
| 12. #14519834 | C4 | semidirect |
| 13. C22⋊#92420 | C4 | semidirect |
| 17. C22⋊#92418 | C4 | semidirect |
| 18. #14519689 | C4 | semidirect |
| 19. C22⋊C8×C61 | C4 | semidirect |
| 23. C22×#6923 | C8 | semidirect |
| 34. C2×#92420 | C2×C4 | semidirect |
| 40. C2×C8×C61 | C2×C4 | semidirect |
| 41. C2×#92418 | C2×C4 | semidirect |
| 75. C22×C61 | C4×C8 | semidirect |
| 81. C2×D61 | C4×C8 | semidirect |
| 87. #6923 | C22⋊C8 | direct (N × H) |
| 105. C61 | C4×C22⋊C8 | semidirect |
| 118. C22⋊C8 | #6923 | direct (N × H) |
| 140. C2×C8 | C2×#6923 | semidirect |
| 184. C22 | C8×#6923 | semidirect |