Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20273400 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1549 | C2 | semidirect |
| 185. #1549 | D53 | semidirect |
| 216. C53 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283352 | 2 |
| #20280537 | 2 |
| #20273400 | 2 |
| #20273027 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| C53×#1549 | 2 |
| #9194 | 53 |