Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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 | C8×C22⋊C4 |
| 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 |
|---|---|---|
| 2. C2×C8×#6923 | C2 | semidirect |
| 4. (C2×#6923)⋊C8 | C2 | semidirect |
| 7. C2×D61⋊C8 | C4 | semidirect |
| 10. C22×#92420 | C4 | semidirect |
| 17. C22⋊#92418 | C4 | semidirect |
| 18. #14519689 | C4 | semidirect |
| 19. C22⋊C8×C61 | C4 | semidirect |
| 30. C22⋊#6923 | C8 | semidirect |
| 51. C2×#6923 | C2×C8 | semidirect |
| 66. #92420 | C22⋊C4 | semidirect |
| 71. C22×C61 | C4×C8 | semidirect |
| 76. C2×D61 | C4×C8 | semidirect |
| 98. C61 | C8×C22⋊C4 | semidirect |
| 110. C22⋊C8 | #6923 | semidirect |
| 171. C22 | C8×#6923 | semidirect |