Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #20276558 | C2 | semidirect |
| 3. #20272782 | C2 | semidirect |
| 4. #20272691 | C2 | semidirect |
| 5. #20272690 | C2 | semidirect |
| 6. #20272637 | C2 | semidirect |
| 7. C53×#2171 | C2 | semidirect |
| 25. #13133163 | C8 | semidirect |
| 26. #13133161 | C8 | semidirect |
| 27. #13133160 | C8 | semidirect |
| 28. #13133158 | C8 | semidirect |
| 100. #2171 | D53 | semidirect |
| 124. C53 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276599 | 2 |
| #20276558 | 2 |
| #20272782 | 2 |
| #20272691 | 2 |
| #20272690 | 2 |
| #20272637 | 2 |
| C53×#2171 | 2 |
| #12068 | 53 |