Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276334 | C2 | semidirect |
| 3. #20272665 | C2 | semidirect |
| 4. #20272653 | C2 | semidirect |
| 5. C53×#1321 | C2 | semidirect |
| 136. #1321 | D53 | semidirect |
| 155. C53 | #11485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283423 | 2 |
| #20276334 | 2 |
| #20272665 | 2 |
| #20272653 | 2 |
| C53×#1321 | 2 |
| #11485 | 53 |