Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
314 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C61 |
| prime radical | C24×C61 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C24×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. C22⋊C4×C61 | Q8 | semidirect |
| 53. #2062 | C61 | direct (N × H) |
| 62. C61 | #2062 | direct (N × H) |
| 83. C22⋊C4 | Q8×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#543 | 2 |
| C61×#385 | 2 |
| C61×#342 | 2 |
| #2062 | 61 |