Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20284746 | C2 | semidirect |
| 3. #20273349 | C2 | semidirect |
| 4. #20273184 | C2 | semidirect |
| 5. #20273059 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#3112 | C2 | semidirect |
| 192. #3112 | D53 | semidirect |
| 229. C53 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285710 | 2 |
| #20284746 | 2 |
| #20273349 | 2 |
| #20273184 | 2 |
| #20273059 | 2 |
| #20272576 | 2 |
| C53×#3112 | 2 |
| #10040 | 53 |