Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #127×C61 | C4 |
| hypercenter | #127 | #6923 |
| hypocenter | C61 | #2931 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519864 | C2 | semidirect |
| 2. #16840797 | C2 | semidirect |
| 3. D4×#92420 | C2 | semidirect |
| 4. #16840766 | C2 | semidirect |
| 5. #16840736 | C2 | semidirect |
| 6. C4×D61⋊C8 | C2 | semidirect |
| 42. D61⋊C8 | D4 | semidirect |
| 74. C4×C61 | #131 | semidirect |
| 91. C61 | #2931 | semidirect |
| 162. C4 | #14519864 | semidirect |