Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
656 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20275277 | C2 | semidirect |
| 4. #20274586 | C2 | semidirect |
| 6. #20274402 | C2 | semidirect |
| 7. C53×#1840 | C2 | semidirect |
| 116. #1840 | D53 | semidirect |
| 141. C53 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278013 | 2 |
| #20275326 | 2 |
| #20275277 | 2 |
| #20274586 | 2 |
| #20274495 | 2 |
| #20274402 | 2 |
| C53×#1840 | 2 |
| #21670 | 53 |