Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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 | C22×C8 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | #103×C61 | C4 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #103 | #6923 |
| hypocenter | C61 | C8×Q16 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #103 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. #11758202 | C8 | semidirect |
| 55. #92420 | Q16 | semidirect |
| 79. C61 | C8×Q16 | semidirect |