Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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 | C2×#125×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×#125 | D61 |
| hypocenter | C61 | C2×#541 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840375 | C2 | direct (N × H) |
| 2. C2×#14519777 | C2 | semidirect |
| 4. C2×#14519768 | C2 | semidirect |
| 6. C2×#14519742 | C2 | semidirect |
| 8. C2×#125×C61 | C2 | semidirect |
| 11. #14519777 | C22 | semidirect |
| 13. #14519768 | C22 | semidirect |
| 15. #14519742 | C22 | semidirect |
| 25. #125×C61 | C22 | semidirect |
| 82. C2×C61 | #541 | semidirect |
| 90. C2×#125 | D61 | semidirect |
| 94. C61 | C2×#541 | semidirect |
| 100. #125 | C2×D61 | semidirect |
| 168. C2 | #16840375 | direct (N × H) |