Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 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×#544 |
| 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. #16840393 | C2 | direct (N × H) |
| 2. C2×#14519776 | C2 | semidirect |
| 3. C2×#14519768 | C2 | semidirect |
| 8. #14519776 | C22 | semidirect |
| 9. #14519768 | C22 | semidirect |
| 24. C22×C4×C61 | Q8 | semidirect |
| 48. C2×C4×C61 | C2×Q8 | semidirect |
| 70. C2×C61 | #544 | semidirect |
| 80. C61 | C2×#544 | semidirect |
| 102. C22×C4 | Dic122 | semidirect |
| 127. C2×C4 | C2×Dic122 | semidirect |
| 143. C2 | #16840393 | direct (N × H) |