Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
1170 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 182 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 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×D4×C19 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×#1749 | C2 | semidirect |
| 3. C2×C19×#329 | C2 | semidirect |
| 13. C2×C19×#97 | C22 | semidirect |
| 90. #8334 | C19 | direct (N × H) |
| 133. #1749 | C2×C19 | semidirect |
| 134. C2×#329 | C2×C19 | semidirect |
| 145. C22×C19 | #329 | semidirect |
| 165. C2×#97 | C22×C19 | semidirect |
| 204. C19 | #8334 | direct (N × H) |
| 301. C22 | C19×#329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C19×#124 | 2 |
| C19×#1749 | 2 |
| C2×C19×#329 | 2 |
| #8334 | 19 |