Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 200 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. #20277032 | C2 | semidirect |
| 3. #20276976 | C2 | semidirect |
| 4. #20272913 | C2 | semidirect |
| 5. #20272907 | C2 | semidirect |
| 6. #20272904 | C2 | semidirect |
| 7. C53×#2178 | C2 | semidirect |
| 96. #2178 | D53 | semidirect |
| 119. C53 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277032 | 2 |
| #20277027 | 2 |
| #20276976 | 2 |
| #20272913 | 2 |
| #20272907 | 2 |
| #20272904 | 2 |
| C53×#2178 | 2 |
| #13691 | 53 |