Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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 | #2935 |
| 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. #16840793 | C2 | semidirect |
| 4. D4×#92420 | C2 | semidirect |
| 5. D61⋊(C4⋊C8) | C2 | semidirect |
| 6. #16840736 | C2 | semidirect |
| 7. C4×#11758213 | C2 | semidirect |
| 49. #11758213 | D4 | semidirect |
| 92. C4×C61 | #131 | semidirect |
| 112. C61 | #2935 | semidirect |
| 201. C4 | #14519864 | semidirect |