Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16810463 | C2 | semidirect |
| 2. C2×#16810461 | C2 | semidirect |
| 3. C2×#16810460 | C2 | semidirect |
| 5. #20276976 | C2 | semidirect |
| 6. C4×#13133123 | C2 | semidirect |
| 7. C53×#2249 | C2 | semidirect |
| 101. #2249 | D53 | semidirect |
| 122. C53 | #13728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| C2×#16810461 | 2 |
| C2×#16810460 | 2 |
| C2×#16810458 | 2 |
| #20276976 | 2 |
| C4×#13133123 | 2 |
| C53×#2249 | 2 |
| #13728 | 53 |