Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1088 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C23×C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | C22⋊#95 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×(C2×#6923)⋊C4 | C2 | semidirect |
| 7. C2×C22⋊#6923 | C4 | semidirect |
| 10. C23×Dic61 | C4 | semidirect |
| 13. C22×C4×D61 | C4 | semidirect |
| 15. C23×C4×C61 | C4 | semidirect |
| 29. C22×#6923 | C2×C4 | semidirect |
| 76. C2×C4×C61 | C22⋊C4 | semidirect |
| 80. C2×Dic61 | C22⋊C4 | semidirect |
| 87. C22×C61 | #95 | semidirect |
| 99. C2×D61 | #95 | semidirect |
| 123. C61 | C22⋊#95 | semidirect |
| 131. C23×C4 | #6923 | semidirect |
| 202. C2×C4 | C22⋊#6923 | semidirect |
| 221. C22 | (C2×#6923)⋊C4 | semidirect |