Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#16810458 | C2 | semidirect |
| 2. #20277009 | C2 | semidirect |
| 3. #20276835 | C2 | semidirect |
| 4. #20272918 | C2 | semidirect |
| 5. #20272905 | C2 | semidirect |
| 6. #20272904 | C2 | semidirect |
| 7. C53×#2221 | C2 | semidirect |
| 92. #2221 | D53 | semidirect |
| 116. C53 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810458 | 2 |
| #20277009 | 2 |
| #20276835 | 2 |
| #20272918 | 2 |
| #20272905 | 2 |
| #20272904 | 2 |
| C53×#2221 | 2 |
| #13700 | 53 |