Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C19 | C2 |
| hypercenter | C4×D4 | D19 |
| hypocenter | C19 | #553 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×D4×C19 | C2 | semidirect |
| 2. #10597385 | C2 | semidirect |
| 3. #10597376 | C2 | semidirect |
| 4. #10597376 | C2 | semidirect |
| 5. #10597372 | C2 | semidirect |
| 6. C2×C4⋊Dic19 | C2 | semidirect |
| 7. #10597344 | C2 | semidirect |
| 8. #10597329 | C2 | semidirect |
| 9. (C22⋊D19)⋊C4 | C2 | semidirect |
| 10. C4×D76 | C2 | semidirect |
| 11. #10597316 | C2 | semidirect |
| 87. C4×D4 | D19 | semidirect |
| 90. C19 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C19 | 2 |
| #10597385 | 2 |
| #10597376 | 2 |
| #10597372 | 2 |
| C2×C4⋊Dic19 | 2 |
| #10597344 | 2 |
| #10597329 | 2 |
| (C22⋊D19)⋊C4 | 2 |
| C4×D76 | 2 |
| #10597316 | 2 |
| #553 | 19 |