Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×C42 | C23×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C19×#2083 | C2 | semidirect |
| 4. C19×#2072 | C2 | semidirect |
| 5. C19×#1272 | C2 | semidirect |
| 6. C19×#1271 | C2 | semidirect |
| 114. #7789 | C19 | direct (N × H) |
| 163. #2083 | C2×C19 | semidirect |
| 164. #2072 | C2×C19 | semidirect |
| 165. #1272 | C2×C19 | semidirect |
| 166. #1271 | C2×C19 | semidirect |
| 254. C19 | #7789 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2732 | 2 |
| C19×#2093 | 2 |
| C19×#2083 | 2 |
| C19×#2072 | 2 |
| C19×#1272 | 2 |
| C19×#1271 | 2 |
| C19×#1270 | 2 |
| #7789 | 19 |