Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
704 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 165 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, socle | C23×C61 | C24 |
| Fitting | C4×C4⋊C4×C61 | C2 |
| hypercenter | C4×C4⋊C4 | D61 |
| hypocenter | C61 | #2544 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519765 | C2 | semidirect |
| 3. C2×#14519765 | C2 | semidirect |
| 4. C2×C4×D244 | C2 | semidirect |
| 5. #16839679 | C2 | semidirect |
| 6. #16839668 | C2 | semidirect |
| 7. #16839664 | C2 | semidirect |
| 8. #16839640 | C2 | semidirect |
| 9. C4×C4⋊C4×C61 | C2 | semidirect |
| 57. C42×C61 | D4 | semidirect |
| 136. C4×C4⋊C4 | D61 | semidirect |
| 137. C61 | #2544 | semidirect |
| 191. C42 | D244 | semidirect |