Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22⋊C4×D19 | C2 | semidirect |
| 3. C19×#99 | C2 | semidirect |
| 4. #10597291 | C2 | semidirect |
| 5. #10597263 | C2 | semidirect |
| 6. C23×D19 | C4 | semidirect |
| 9. C2×C22⋊D19 | C4 | semidirect |
| 13. C2×D76 | C4 | semidirect |
| 15. C2×C4×D19 | C4 | semidirect |
| 16. C22⋊C4×C19 | C22 | semidirect |
| 17. C22⋊Dic19 | C22 | semidirect |
| 19. C23×C19 | C2×C4 | semidirect |
| 27. C22×D19 | C2×C4 | semidirect |
| 32. C2×C4×C19 | C2×C4 | semidirect |
| 36. C2×Dic19 | C2×C4 | semidirect |
| 69. D19 | #99 | direct (N × H) |
| 74. #99 | D19 | direct (N × H) |
| 75. C19 | C2×#99 | semidirect |
| 88. C22⋊C4 | C2×D19 | semidirect |
| 98. C23 | C4×D19 | semidirect |
| 110. C2×C4 | C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D19 | 2 |
| C22⋊C4×D19 | 2 |
| C19×#99 | 2 |
| #10597291 | 2 |
| #10597263 | 2 |
| C2×#99 | 19 |