Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×C8 | C22×D61 |
| commutator | C2×C61 | C22×C16 |
| Fitting | C61×C4⋊C16 | C2 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C4⋊C16 | D61 |
| hypocenter | C61 | D4×C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C4⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C16×D61 | C2 | semidirect |
| 3. #16839541 | C2 | semidirect |
| 4. C4×#11758185 | C2 | semidirect |
| 5. C61×C4⋊C16 | C2 | semidirect |
| 27. #11758185 | D4 | semidirect |
| 33. D244 | C16 | semidirect |
| 43. C2×D61 | C2×C16 | semidirect |
| 45. C4×C61 | C2×C16 | semidirect |
| 56. C4⋊C16 | D61 | semidirect |
| 59. C61 | D4×C16 | semidirect |
| 100. C4 | C16×D61 | semidirect |