Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. Q64×D53 | C2 | semidirect |
| 3. #20272932 | C2 | semidirect |
| 4. #20272931 | C2 | semidirect |
| 5. #20272929 | C2 | semidirect |
| 6. #20272925 | C2 | semidirect |
| 7. C53×Q128 | C2 | semidirect |
| 63. Q128 | D53 | semidirect |
| 81. C53 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277025 | 2 |
| Q64×D53 | 2 |
| #20272932 | 2 |
| #20272931 | 2 |
| #20272929 | 2 |
| #20272925 | 2 |
| C53×Q128 | 2 |
| #13743 | 53 |