Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C4×C22⋊C4×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C4×C22⋊C4 | D61 |
| hypocenter | C61 | C8×C22⋊C4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×#92418 | C2 | semidirect |
| 4. #16839517 | C2 | semidirect |
| 7. C22×#92418 | C4 | semidirect |
| 11. C22⋊#92418 | C4 | semidirect |
| 25. C22⋊C4×C61 | C8 | semidirect |
| 48. C2×C4×C61 | C2×C8 | semidirect |
| 55. #92418 | C22⋊C4 | direct (N × H) |
| 59. C22×C61 | C4×C8 | semidirect |
| 80. C61 | C8×C22⋊C4 | semidirect |
| 108. C22⋊C4 | #92418 | direct (N × H) |
| 122. C2×C4 | C2×#92418 | semidirect |
| 134. C22 | C4×#92418 | semidirect |