Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C22⋊Q8×C61 | C4 |
| hypercenter | C22⋊Q8 | #6923 |
| hypocenter | C61 | #2995 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840813 | C2 | semidirect |
| 2. #16840795 | C2 | semidirect |
| 3. #16840794 | C2 | semidirect |
| 4. #16840792 | C2 | semidirect |
| 5. #16840787 | C2 | semidirect |
| 6. #16840782 | C2 | semidirect |
| 7. #16840769 | C2 | semidirect |
| 8. #16840765 | C2 | semidirect |
| 124. C61 | #2995 | semidirect |