Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
856 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#2646 | C2 | semidirect |
| 4. C19×#1294 | C2 | semidirect |
| 5. C19×#1280 | C2 | semidirect |
| 90. #10344 | C19 | direct (N × H) |
| 148. #2646 | C2×C19 | semidirect |
| 151. #1294 | C2×C19 | semidirect |
| 152. #1280 | C2×C19 | semidirect |
| 231. C19 | #10344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2646 | 2 |
| C19×#1786 | 2 |
| C19×#1438 | 2 |
| C19×#1294 | 2 |
| C19×#1280 | 2 |
| #10344 | 19 |