Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
404 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #20276665 | C2 | semidirect |
| 2. #20276660 | C2 | semidirect |
| 3. #20275819 | C2 | semidirect |
| 4. #20272709 | C2 | semidirect |
| 5. #20272706 | C2 | semidirect |
| 6. #20272653 | C2 | semidirect |
| 7. C53×#3204 | C2 | semidirect |
| 185. #3204 | D53 | semidirect |
| 217. C53 | #12119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276665 | 2 |
| #20276660 | 2 |
| #20275819 | 2 |
| #20272709 | 2 |
| #20272706 | 2 |
| #20272653 | 2 |
| C53×#3204 | 2 |
| #12119 | 53 |