Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C4×C4⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C4×C4⋊C4 | D61 |
| hypocenter | C61 | #2337 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839666 | C2 | semidirect |
| 3. #16839653 | C2 | semidirect |
| 4. #16839652 | C2 | semidirect |
| 6. #16839633 | C2 | semidirect |
| 7. #16839630 | C2 | semidirect |
| 8. C4×#11758198 | C2 | semidirect |
| 9. C4×C4⋊C4×C61 | C2 | semidirect |
| 13. #14519765 | C4 | semidirect |
| 47. C2×Dic122 | C2×C4 | semidirect |
| 51. C42×C61 | C2×C4 | semidirect |
| 55. #11758198 | C2×C4 | semidirect |
| 56. #11758198 | C2×C4 | semidirect |
| 126. C4×C4⋊C4 | D61 | semidirect |
| 128. C61 | #2337 | semidirect |
| 177. C42 | C4×D61 | semidirect |