Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C22×C61 | C22×C8 |
| Fitting | C2×C4×D4×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C4×D4 | D61 |
| hypocenter | C61 | #1869 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#92418 | C2 | semidirect |
| 2. C2×C22⋊#92418 | C2 | semidirect |
| 3. C2×C22⋊#92418 | C2 | semidirect |
| 4. #16839517 | C2 | semidirect |
| 25. C2×D4×C61 | C8 | semidirect |
| 50. C2×#92418 | D4 | semidirect |
| 59. C23×C61 | C2×C8 | semidirect |
| 77. C2×C4×C61 | C2×C8 | semidirect |
| 93. C22×C61 | C22⋊C8 | semidirect |
| 119. C61 | #1869 | semidirect |
| 139. C2×D4 | #92418 | semidirect |
| 172. C23 | C2×#92418 | semidirect |
| 190. C2×C4 | C2×#92418 | semidirect |
| 207. C22 | C22⋊#92418 | semidirect |