Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 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 | C2×C4×Q8×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic61 | C2 | semidirect |
| 3. #16839668 | C2 | semidirect |
| 4. #16839667 | C2 | semidirect |
| 7. C2×C4×Q8×C61 | C2 | semidirect |
| 11. C2×Q8×D61 | C4 | semidirect |
| 45. #11758198 | Q8 | direct (N × H) |
| 56. Q8×C61 | C22⋊C4 | semidirect |
| 65. C2×C4×C61 | C2×Q8 | semidirect |
| 74. C2×Dic61 | C2×Q8 | semidirect |
| 90. C2×D61 | C4×Q8 | semidirect |
| 108. C2×C4×Q8 | D61 | semidirect |
| 113. C61 | Q8×C22⋊C4 | semidirect |
| 163. Q8 | #11758198 | direct (N × H) |
| 181. C2×C4 | Q8×D61 | semidirect |