Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #20280594 | C2 | semidirect |
| 4. #20273341 | C2 | semidirect |
| 5. #20273161 | C2 | semidirect |
| 6. #20272579 | C2 | semidirect |
| 222. C53 | #10021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285115 | 2 |
| #20284833 | 2 |
| #20280594 | 2 |
| #20273341 | 2 |
| #20273161 | 2 |
| #20272579 | 2 |
| C53×#1514 | 2 |
| #10021 | 53 |