Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D61 |
| commutator | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C22×C4⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C22×C4⋊C4 | D61 |
| hypocenter | C61 | C2×#537 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758222 | C2 | semidirect |
| 2. #16840343 | C2 | direct (N × H) |
| 3. C2×#14519757 | C2 | semidirect |
| 4. C2×#14519752 | C2 | semidirect |
| 5. C2×#14519751 | C2 | semidirect |
| 6. C22×C4⋊C4×C61 | C2 | semidirect |
| 8. C2×#11758222 | C22 | semidirect |
| 14. #14519757 | C22 | semidirect |
| 15. #14519752 | C22 | semidirect |
| 16. #14519751 | C22 | semidirect |
| 22. C2×C4⋊C4×C61 | C22 | semidirect |
| 26. C22×C4×C61 | D4 | semidirect |
| 58. C2×C4×C61 | C2×D4 | semidirect |
| 85. C2×C61 | #537 | semidirect |
| 95. C22×C4⋊C4 | D61 | semidirect |
| 96. C61 | C2×#537 | semidirect |
| 111. C2×C4⋊C4 | C2×D61 | semidirect |
| 128. C22×C4 | D244 | semidirect |
| 155. C2×C4 | C2×D244 | semidirect |
| 175. C2 | #16840343 | direct (N × H) |