Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20276508 | C2 | semidirect |
| 3. #20272922 | C2 | semidirect |
| 4. #20272921 | C2 | semidirect |
| 5. #20272905 | C2 | semidirect |
| 6. #20272854 | C2 | semidirect |
| 7. C53×#1419 | C2 | semidirect |
| 85. #1419 | D53 | semidirect |
| 102. C53 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276815 | 2 |
| #20276508 | 2 |
| #20272922 | 2 |
| #20272921 | 2 |
| #20272905 | 2 |
| #20272854 | 2 |
| C53×#1419 | 2 |
| #13717 | 53 |