Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 105 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×#121 | C2 |
| hypercenter | #121 | D19 |
| hypocenter | C19 | #550 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64543 | C2 | semidirect |
| 2. C2×#64541 | C2 | semidirect |
| 3. C19×#121 | C2 | semidirect |
| 4. #10597386 | C2 | semidirect |
| 5. #10597386 | C2 | semidirect |
| 6. #10597385 | C2 | semidirect |
| 7. C4×C22⋊D19 | C2 | semidirect |
| 8. #10597341 | C2 | semidirect |
| 9. #10597333 | C2 | semidirect |
| 10. #10597330 | C2 | semidirect |
| 11. (C22⋊D19)⋊C4 | C2 | semidirect |
| 61. Dic38 | D4 | semidirect |
| 81. Dic19 | #41 | semidirect |
| 97. #121 | D19 | semidirect |
| 101. C19 | #550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64543 | 2 |
| C2×#64541 | 2 |
| C19×#121 | 2 |
| #10597386 | 2 |
| #10597385 | 2 |
| C4×C22⋊D19 | 2 |
| #10597341 | 2 |
| #10597333 | 2 |
| #10597330 | 2 |
| (C22⋊D19)⋊C4 | 2 |
| #550 | 19 |