Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#500 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #500 | D61 |
| hypocenter | C61 | #3164 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840170 | C2 | semidirect |
| 3. #16840168 | C2 | semidirect |
| 4. #16840166 | C2 | semidirect |
| 5. #16840164 | C2 | semidirect |
| 6. #16840163 | C2 | semidirect |
| 11. C61×#500 | C2 | semidirect |
| 66. #11758189 | Q8 | semidirect |
| 67. C8×D61 | Q8 | semidirect |
| 112. #500 | D61 | semidirect |
| 119. C61 | #3164 | semidirect |