Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20276386 | C2 | semidirect |
| 3. #20276365 | C2 | semidirect |
| 4. #20275262 | C2 | semidirect |
| 5. #20275001 | C2 | semidirect |
| 6. #20272843 | C2 | semidirect |
| 7. C53×#1910 | C2 | semidirect |
| 199. #1910 | D53 | semidirect |
| 230. C53 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285576 | 2 |
| #20276386 | 2 |
| #20276365 | 2 |
| #20275262 | 2 |
| #20275001 | 2 |
| #20272843 | 2 |
| C53×#1910 | 2 |
| #13432 | 53 |