Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×#125 | C2 |
| prime radical | C22×D19 | C23 |
| hypercenter | #125 | D19 |
| hypocenter | C19 | #541 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#125 | C2 | semidirect |
| 8. #10597336 | C2 | semidirect |
| 9. #10597335 | C2 | semidirect |
| 10. #10597335 | C2 | semidirect |
| 11. #10597335 | C2 | semidirect |
| 12. #10597334 | C2 | semidirect |
| 13. #10597333 | C2 | semidirect |
| 15. C4×Dic38 | C2 | semidirect |
| 101. #125 | D19 | semidirect |
| 107. C19 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#125 | 2 |
| #10597344 | 2 |
| #10597342 | 2 |
| #10597338 | 2 |
| #10597336 | 2 |
| #10597335 | 2 |
| #10597334 | 2 |
| #10597333 | 2 |
| #10597322 | 2 |
| C4×Dic38 | 2 |
| #541 | 19 |