Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
426 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C19 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×M16×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#3197 | C2 | semidirect |
| 2. C19×#2191 | C2 | semidirect |
| 3. C19×#2190 | C2 | semidirect |
| 4. C19×#2010 | C2 | semidirect |
| 5. C19×#1340 | C2 | semidirect |
| 6. C19×#1339 | C2 | semidirect |
| 7. C19×#1320 | C2 | semidirect |
| 34. C2×Q16×C19 | D4 | semidirect |
| 36. C2×D8×C19 | D4 | semidirect |
| 61. C19×#106 | D4 | semidirect |
| 62. C19×#106 | D4 | semidirect |
| 126. #12116 | C19 | direct (N × H) |
| 167. #3197 | C2×C19 | semidirect |
| 168. #2191 | C2×C19 | semidirect |
| 169. #2190 | C2×C19 | semidirect |
| 170. #2010 | C2×C19 | semidirect |
| 171. #1340 | C2×C19 | semidirect |
| 172. #1339 | C2×C19 | semidirect |
| 173. #1320 | C2×C19 | semidirect |
| 228. C2×Q16 | D4×C19 | semidirect |
| 230. C2×D8 | D4×C19 | semidirect |
| 255. #106 | D4×C19 | semidirect |
| 256. #106 | D4×C19 | semidirect |
| 264. C19 | #12116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#3197 | 2 |
| C19×#2191 | 2 |
| C19×#2190 | 2 |
| C19×#2010 | 2 |
| C19×#1340 | 2 |
| C19×#1339 | 2 |
| C19×#1320 | 2 |
| #12116 | 19 |