Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #20263319 | C2 | semidirect |
| 2. #20263319 | C2 | semidirect |
| 3. #20263312 | C2 | semidirect |
| 4. #20263310 | C2 | semidirect |
| 5. #20263309 | C2 | semidirect |
| 6. #20263308 | C2 | semidirect |
| 7. #20263305 | C2 | semidirect |
| 8. #20263303 | C2 | semidirect |
| 10. C4×C22⋊D197 | C2 | semidirect |
| 11. #20263286 | C2 | semidirect |
| 12. #20263285 | C2 | semidirect |
| 13. #20263282 | C2 | semidirect |
| 14. C2×C22⋊Dic197 | C2 | semidirect |
| 15. C2×C22⋊C4×C197 | C2 | semidirect |
| 16. C2×Dic394 | C22 | semidirect |
| 22. C2×C4×D197 | C22 | semidirect |
| 23. C4⋊Dic197 | C22 | semidirect |
| 24. C4⋊Dic197 | C22 | semidirect |
| 25. C4⋊Dic197 | C22 | semidirect |
| 26. #15691337 | C22 | semidirect |
| 27. #15691337 | C22 | semidirect |
| 28. #15691337 | C22 | semidirect |
| 29. #15691337 | C22 | semidirect |
| 30. #15691337 | C22 | semidirect |
| 38. #15691335 | C22 | semidirect |
| 39. #15691335 | C22 | semidirect |
| 40. #15691335 | C22 | semidirect |
| 41. C4×Dic197 | C22 | semidirect |
| 42. C4×Dic197 | C22 | semidirect |
| 43. C4×Dic197 | C22 | semidirect |
| 110. C197 | #551 | semidirect |
| 126. C2×C22⋊C4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263319 | 2 |
| #20263312 | 2 |
| #20263310 | 2 |
| #20263309 | 2 |
| #20263308 | 2 |
| #20263305 | 2 |
| #20263303 | 2 |
| #20263295 | 2 |
| C4×C22⋊D197 | 2 |
| #20263286 | 2 |
| #20263285 | 2 |
| #20263282 | 2 |
| C2×C22⋊Dic197 | 2 |
| C2×C22⋊C4×C197 | 2 |
| #551 | 197 |