Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275697 | C2 | semidirect |
| 3. #20273446 | C2 | semidirect |
| 5. #20273228 | C2 | semidirect |
| 7. C53×#1537 | C2 | semidirect |
| 11. #16811347 | C4 | semidirect |
| 14. #16811288 | C4 | semidirect |
| 206. #1537 | D53 | semidirect |
| 239. C53 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289126 | 2 |
| #20275697 | 2 |
| #20273446 | 2 |
| #20273438 | 2 |
| #20273228 | 2 |
| #20273224 | 2 |
| C53×#1537 | 2 |
| #8496 | 53 |