Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#423 | C2 |
| hypercenter | #423 | D61 |
| hypocenter | C61 | #2931 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519785 | C2 | semidirect |
| 3. #16839839 | C2 | semidirect |
| 4. #16839827 | C2 | semidirect |
| 5. #16839730 | C2 | semidirect |
| 6. C2×C4×#92418 | C2 | semidirect |
| 7. C61×#423 | C2 | semidirect |
| 42. C2×#92418 | D4 | semidirect |
| 75. C4×C61 | #131 | semidirect |
| 88. #423 | D61 | semidirect |
| 91. C61 | #2931 | semidirect |
| 160. C4 | #14519785 | semidirect |