Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
316 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C4⋊C8×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | C4⋊C8 | #6923 |
| hypocenter | C61 | C4×C4⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #14519844 | C4 | semidirect |
| 12. C4⋊#92420 | C4 | semidirect |
| 16. C4⋊#92418 | C4 | semidirect |
| 17. #14519706 | C4 | semidirect |
| 18. C4⋊C8×C61 | C4 | semidirect |
| 28. C4×#6923 | C8 | semidirect |
| 69. #6923 | C4⋊C8 | direct (N × H) |
| 71. C4×C61 | C4×C8 | semidirect |
| 75. Dic61 | C4×C8 | semidirect |
| 89. C61 | C4×C4⋊C8 | semidirect |
| 101. C4⋊C8 | #6923 | direct (N × H) |
| 159. C4 | C8×#6923 | semidirect |