Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #20293105 | C2 | semidirect |
| 3. #20292728 | C2 | semidirect |
| 4. SD16×Dic107 | C2 | semidirect |
| 5. #20292665 | C2 | semidirect |
| 6. #20292636 | C2 | semidirect |
| 8. #20292582 | C2 | semidirect |
| 12. Q8×Dic107 | C22 | semidirect |
| 20. #16812043 | C22 | semidirect |
| 21. #16812041 | C22 | semidirect |
| 22. #16812033 | C22 | semidirect |
| 24. #16812019 | C22 | semidirect |
| 25. C8×Dic107 | C22 | semidirect |
| 28. C2×SD16×C107 | C4 | semidirect |
| 50. C2×Q8×C107 | C2×C4 | semidirect |
| 58. SD16×C107 | C2×C4 | semidirect |
| 59. SD16×C107 | C2×C4 | semidirect |
| 60. C2×C8×C107 | C2×C4 | semidirect |
| 104. C107 | #2949 | semidirect |
| 116. C2×SD16 | Dic107 | semidirect |
| 139. C2×Q8 | C2×Dic107 | semidirect |
| 148. SD16 | C2×Dic107 | semidirect |
| 149. SD16 | C2×Dic107 | semidirect |
| 152. C2×C8 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293105 | 2 |
| #20293102 | 2 |
| #20292728 | 2 |
| SD16×Dic107 | 2 |
| #20292665 | 2 |
| #20292636 | 2 |
| #20292632 | 2 |
| #20292582 | 2 |
| C22×SD16×C107 | 2 |
| #2949 | 107 |