Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | #102×C61 | C4 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #102 | #6923 |
| hypocenter | C61 | #1762 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14519831 | C2 | semidirect |
| 4. C4⋊C4×#6923 | C2 | semidirect |
| 5. #16840636 | C2 | semidirect |
| 6. #16840635 | C2 | semidirect |
| 11. D4×#6923 | C4 | semidirect |
| 17. #14519839 | C4 | semidirect |
| 23. #14519699 | C4 | semidirect |
| 24. #14519698 | C4 | semidirect |
| 25. #14519697 | C4 | semidirect |
| 26. #102×C61 | C4 | semidirect |
| 49. C4⋊#6923 | C2×C4 | semidirect |
| 54. D61⋊C8 | C2×C4 | semidirect |
| 55. C2×C8×C61 | C2×C4 | semidirect |
| 56. C4⋊C4×C61 | C2×C4 | semidirect |
| 57. C4⋊Dic61 | C2×C4 | semidirect |
| 59. C2×#92418 | C2×C4 | semidirect |
| 85. D4×C61 | C42 | semidirect |
| 93. D244 | C42 | semidirect |
| 147. C61 | #1762 | semidirect |
| 164. #102 | #6923 | semidirect |
| 190. C2×C8 | C2×#6923 | semidirect |
| 197. C4⋊C4 | C2×#6923 | semidirect |
| 216. D4 | C4×#6923 | semidirect |