Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 183 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×#16810829 | C2 | semidirect |
| 3. #20277434 | C2 | semidirect |
| 4. #20276135 | C2 | semidirect |
| 6. #20275069 | C2 | semidirect |
| 7. #20274726 | C2 | semidirect |
| 8. C53×#1832 | C2 | semidirect |
| 36. #13133217 | D4 | semidirect |
| 153. #1832 | D53 | semidirect |
| 179. C53 | #28166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810829 | 2 |
| #20277440 | 2 |
| #20277434 | 2 |
| #20276135 | 2 |
| #20275805 | 2 |
| #20275069 | 2 |
| #20274726 | 2 |
| C53×#1832 | 2 |
| #28166 | 53 |