Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276364 | C2 | semidirect |
| 4. #20275262 | C2 | semidirect |
| 5. #20275242 | C2 | semidirect |
| 6. #20272844 | C2 | semidirect |
| 7. C53×#1868 | C2 | semidirect |
| 200. #1868 | 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 |
|---|---|
| #20285580 | 2 |
| #20276386 | 2 |
| #20276364 | 2 |
| #20275262 | 2 |
| #20275242 | 2 |
| #20272844 | 2 |
| C53×#1868 | 2 |
| #13432 | 53 |