Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 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 | C23×Q8×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C23×Q8 | D61 |
| hypocenter | C61 | C22×#124 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519766 | C2 | direct (N × H) |
| 3. C22×#11758198 | C2 | semidirect |
| 4. C22×C4×Dic61 | C2 | semidirect |
| 5. C23×Q8×C61 | C2 | semidirect |
| 10. #14519766 | C22 | direct (N × H) |
| 11. C2×#11758198 | C22 | semidirect |
| 12. C2×C4×Dic61 | C22 | semidirect |
| 14. C22×Q8×C61 | C22 | semidirect |
| 22. C2×Q8×C61 | C23 | semidirect |
| 31. #11758198 | C23 | semidirect |
| 32. C4×Dic61 | C23 | semidirect |
| 48. C22×C61 | #124 | semidirect |
| 59. C2×C61 | C2×#124 | semidirect |
| 63. C23×Q8 | D61 | semidirect |
| 68. C61 | C22×#124 | semidirect |
| 71. C22×Q8 | C2×D61 | semidirect |
| 85. C2×Q8 | C22×D61 | semidirect |
| 114. C22 | #14519766 | direct (N × H) |
| 122. C2 | C2×#14519766 | direct (N × H) |