Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261543 | C2 | semidirect |
| 2. #20261537 | C2 | semidirect |
| 3. #20261120 | C2 | semidirect |
| 4. #20261007 | C2 | semidirect |
| 5. #20261005 | C2 | semidirect |
| 6. #20261000 | C2 | semidirect |
| 7. #20260911 | C2 | semidirect |
| 8. #20260908 | C2 | semidirect |
| 9. #20260852 | C2 | semidirect |
| 10. #20260850 | C2 | semidirect |
| 11. #578×C97 | C2 | semidirect |
| 18. #15690835 | C22 | semidirect |
| 23. C2×#13095498 | C22 | semidirect |
| 26. #15690817 | C22 | semidirect |
| 28. #15690799 | C22 | semidirect |
| 29. #15690746 | C22 | semidirect |
| 30. #15690745 | C22 | semidirect |
| 31. #15690737 | C22 | semidirect |
| 32. #15690737 | C22 | semidirect |
| 34. #15690729 | C22 | semidirect |
| 35. #15690726 | C22 | semidirect |
| 36. C8×Dic97 | C22 | semidirect |
| 37. 2−1+4×C97 | C22 | semidirect |
| 39. #137×C97 | C22 | semidirect |
| 43. C2×Q16×C97 | C22 | semidirect |
| 44. #131×C97 | C22 | semidirect |
| 150. C97 | #3290 | semidirect |
| 151. #578 | D97 | semidirect |
| 162. 2−1+4 | C2×D97 | semidirect |
| 167. #137 | C2×D97 | semidirect |
| 178. C2×Q16 | C2×D97 | semidirect |
| 185. #131 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261543 | 2 |
| #20261537 | 2 |
| #20261120 | 2 |
| #20261007 | 2 |
| #20261005 | 2 |
| #20261000 | 2 |
| #20260911 | 2 |
| #20260908 | 2 |
| #20260852 | 2 |
| #20260850 | 2 |
| #578×C97 | 2 |
| #3290 | 97 |