Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
176 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D244 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#322 | C2 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #322 | D61 |
| hypocenter | C61 | SD16⋊C8 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 ◁ #322 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C8×Dic122 | C2 | semidirect |
| 4. #16839515 | C2 | semidirect |
| 5. #16839494 | C2 | semidirect |
| 7. C61×#322 | C2 | semidirect |
| 39. #11758190 | C8 | semidirect |
| 53. Dic122 | C2×C8 | semidirect |
| 58. C8×C61 | C2×C8 | semidirect |
| 84. #322 | D61 | semidirect |
| 85. C61 | SD16⋊C8 | semidirect |
| 138. C8 | C8×D61 | semidirect |