Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×D19 | C2 | semidirect |
| 2. C2×#64543 | C2 | semidirect |
| 3. C19×AGL(1,ℤ/8) | C2 | semidirect |
| 4. #10597397 | C2 | semidirect |
| 5. #10597378 | C2 | semidirect |
| 6. #10597362 | C2 | semidirect |
| 7. #10597361 | C2 | semidirect |
| 8. #10597358 | C2 | semidirect |
| 9. #10597357 | C2 | semidirect |
| 10. #10597355 | C2 | semidirect |
| 11. M16×D19 | C2 | semidirect |
| 13. C2×D4×C19 | C22 | semidirect |
| 16. #64545 | C22 | semidirect |
| 17. Q8×D19 | C22 | semidirect |
| 22. #64543 | C22 | semidirect |
| 23. #64543 | C22 | semidirect |
| 25. D4×D19 | C22 | semidirect |
| 30. C2×Dic38 | C22 | semidirect |
| 31. SD16×C19 | C22 | semidirect |
| 32. D8×C19 | C22 | semidirect |
| 33. M16×C19 | C22 | semidirect |
| 34. #64528 | C22 | semidirect |
| 35. #64526 | C22 | semidirect |
| 36. #64526 | C22 | semidirect |
| 37. #64525 | C22 | semidirect |
| 38. #64520 | C22 | semidirect |
| 39. Dic76 | C22 | semidirect |
| 40. #64516 | C22 | semidirect |
| 41. #64515 | C22 | semidirect |
| 42. C8×D19 | C22 | semidirect |
| 109. AGL(1,ℤ/8) | D19 | semidirect |
| 113. C19 | #575 | semidirect |
| 129. C2×D4 | C2×D19 | semidirect |
| 138. SD16 | C2×D19 | semidirect |
| 140. D8 | C2×D19 | semidirect |
| 143. M16 | C2×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D19 | 2 |
| C2×#64543 | 2 |
| C19×AGL(1,ℤ/8) | 2 |
| #10597397 | 2 |
| #10597378 | 2 |
| #10597362 | 2 |
| #10597361 | 2 |
| #10597358 | 2 |
| #10597357 | 2 |
| #10597355 | 2 |
| M16×D19 | 2 |
| #575 | 19 |