Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C24×C4×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C24×C4 | D61 |
| hypocenter | C61 | C22×#123 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519760 | C2 | direct (N × H) |
| 3. C22×#11758196 | C2 | semidirect |
| 4. C22×C22⋊Dic61 | C2 | semidirect |
| 5. C22×#11758198 | C2 | semidirect |
| 6. C24×C4×C61 | C2 | semidirect |
| 12. #14519760 | C22 | direct (N × H) |
| 13. C2×#11758196 | C22 | semidirect |
| 14. C2×C22⋊Dic61 | C22 | semidirect |
| 15. C2×#11758198 | C22 | semidirect |
| 19. C23×C4×C61 | C22 | semidirect |
| 30. C22×C4×C61 | C23 | semidirect |
| 37. C22⋊Dic61 | C23 | semidirect |
| 38. #11758198 | C23 | semidirect |
| 39. #11758196 | C23 | semidirect |
| 61. C22×C61 | #123 | semidirect |
| 74. C2×C61 | C2×#123 | semidirect |
| 79. C24×C4 | D61 | semidirect |
| 84. C61 | C22×#123 | semidirect |
| 93. C23×C4 | C2×D61 | semidirect |
| 114. C22×C4 | C22×D61 | semidirect |
| 142. C22 | #14519760 | direct (N × H) |
| 152. C2 | C2×#14519760 | direct (N × H) |