Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C22×#6923 |
| commutator, socle | C22×C61 | C2×C42 |
| Fitting | C22⋊C8×C61 | C4 |
| hypercenter | C22⋊C8 | #6923 |
| hypocenter | C61 | #1454 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #92420⋊C8 | C2 | semidirect |
| 4. #92420⋊C8 | C2 | semidirect |
| 5. #16840603 | C2 | semidirect |
| 6. C8×#92420 | C2 | semidirect |
| 80. C61 | #1454 | semidirect |