Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
702 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20275279 | C2 | semidirect |
| 4. #20274860 | C2 | semidirect |
| 5. C8×#11719919 | C2 | semidirect |
| 7. C53×#1726 | C2 | semidirect |
| 119. #1726 | D53 | semidirect |
| 141. C53 | #21668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278013 | 2 |
| #20275328 | 2 |
| #20275279 | 2 |
| #20274860 | 2 |
| C8×#11719919 | 2 |
| C8×#11719921 | 2 |
| C53×#1726 | 2 |
| #21668 | 53 |