Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 79 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. M64×D53 | C2 | semidirect |
| 3. #368×D53 | C2 | semidirect |
| 4. #20272909 | C2 | semidirect |
| 5. #20272907 | C2 | semidirect |
| 6. #20272905 | C2 | semidirect |
| 7. C53×#1419 | C2 | semidirect |
| 122. #1419 | D53 | semidirect |
| 145. C53 | #13625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811052 | 2 |
| M64×D53 | 2 |
| #368×D53 | 2 |
| #20272909 | 2 |
| #20272907 | 2 |
| #20272905 | 2 |
| C53×#1419 | 2 |
| #13625 | 53 |