Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 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. #20277033 | C2 | semidirect |
| 3. #20276597 | C2 | semidirect |
| 4. #20272913 | C2 | semidirect |
| 5. #20272908 | C2 | semidirect |
| 6. #20272905 | C2 | semidirect |
| 7. C53×#2249 | C2 | semidirect |
| 95. #2249 | 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 |
|---|---|
| #20277033 | 2 |
| #20277028 | 2 |
| #20276597 | 2 |
| #20272913 | 2 |
| #20272908 | 2 |
| #20272905 | 2 |
| C53×#2249 | 2 |
| #13691 | 53 |