Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C22×D4×C19 | C2 | semidirect |
| 2. C2×#64541 | C2 | semidirect |
| 3. C2×#64526 | C2 | semidirect |
| 4. #10597378 | C2 | direct (N × H) |
| 5. C2×#64525 | C2 | semidirect |
| 6. C2×#64520 | C2 | semidirect |
| 11. C2×D4×C19 | C22 | semidirect |
| 15. #64541 | C22 | semidirect |
| 16. C2×D76 | C22 | semidirect |
| 18. C2×Dic38 | C22 | semidirect |
| 19. #64526 | C22 | semidirect |
| 20. #64525 | C22 | semidirect |
| 21. #64520 | C22 | semidirect |
| 22. C2×C19⋊C8 | C22 | semidirect |
| 38. D76 | C23 | semidirect |
| 41. Dic38 | C23 | semidirect |
| 42. C19⋊C8 | C23 | semidirect |
| 58. C2×C19 | AGL(1,ℤ/8) | semidirect |
| 62. C22×D4 | D19 | semidirect |
| 67. C19 | C2×AGL(1,ℤ/8) | semidirect |
| 77. C2×D4 | C2×D19 | semidirect |
| 119. C2 | #10597378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C19 | 2 |
| C2×#64541 | 2 |
| C2×#64526 | 2 |
| #10597378 | 2 |
| C2×#64525 | 2 |
| C2×#64520 | 2 |
| C2×AGL(1,ℤ/8) | 19 |