Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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 | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#441 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #441 | D61 |
| hypocenter | C61 | #2943 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#11758226 | C2 | semidirect |
| 3. #16839875 | C2 | semidirect |
| 4. #16839873 | C2 | semidirect |
| 5. #16839869 | C2 | semidirect |
| 6. #16839865 | C2 | semidirect |
| 7. #16839860 | C2 | semidirect |
| 8. #16839797 | C2 | semidirect |
| 9. #16839757 | C2 | semidirect |
| 10. #97×D61 | C2 | semidirect |
| 11. C61×#441 | C2 | semidirect |
| 13. #14519800 | C4 | semidirect |
| 42. #11758226 | C2×C4 | semidirect |
| 50. Q16×C61 | C2×C4 | semidirect |
| 57. #11758201 | C2×C4 | semidirect |
| 69. D488 | C2×C4 | semidirect |
| 71. C8×D61 | C2×C4 | semidirect |
| 120. #441 | D61 | semidirect |
| 126. C61 | #2943 | semidirect |
| 165. Q16 | C4×D61 | semidirect |