Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
992 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊#6923 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | C25×C61 | C4 |
| socle | C23×C61 | C22⋊C4 |
| hypercenter | C25 | #6923 |
| hypocenter | C61 | C22×#100 |
| LCS | G ▷ C22×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C24 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758217 | C2 | semidirect |
| 2. C2×#14519837 | C2 | direct (N × H) |
| 5. C2×#11758217 | C22 | semidirect |
| 7. #14519837 | C22 | direct (N × H) |
| 35. #11758217 | C23 | semidirect |
| 68. C22×C61 | #100 | semidirect |
| 82. C2×C61 | C2×#100 | semidirect |
| 88. C61 | C22×#100 | semidirect |
| 157. C22 | #14519837 | direct (N × H) |
| 167. C2 | C2×#14519837 | direct (N × H) |