Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
764 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #342 |
| commutator | C24 | C42×C19 |
| Frattini, cosocle | C23×D4 | C22×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C24 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ C23×D4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C22×C22⋊C4×C19 | C4 | semidirect |
| 8. C2×C19×#100 | C4 | semidirect |
| 10. C2×C19×#99 | C4 | semidirect |
| 89. #7304 | C19 | direct (N × H) |
| 196. C22×C22⋊C4 | C4×C19 | semidirect |
| 198. C2×#100 | C4×C19 | semidirect |
| 200. C2×#99 | C4×C19 | semidirect |
| 238. C19 | #7304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#1783 | 2 |
| C19×#1781 | 2 |
| C19×#1438 | 2 |
| #7304 | 19 |