Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D61 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C61×#364 | C2 |
| socle | C2×C61 | C2×C4⋊C8 |
| hypercenter | #364 | D61 |
| hypocenter | C61 | C2×#364 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #364 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16839583 | C2 | semidirect |
| 4. #16839582 | C2 | semidirect |
| 5. C61×#364 | C2 | semidirect |
| 64. D61 | #364 | direct (N × H) |
| 69. #364 | D61 | direct (N × H) |
| 70. C61 | C2×#364 | semidirect |