Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 67 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×D1696 | C2 | semidirect |
| 2. C2×#16810458 | C2 | semidirect |
| 3. #20276963 | C2 | semidirect |
| 4. C32×Dic53 | C2 | semidirect |
| 5. C2×C53×D32 | C2 | semidirect |
| 24. #13133123 | D4 | semidirect |
| 29. C32×C53 | D4 | semidirect |
| 64. Dic53 | D32 | semidirect |
| 67. C2×D32 | D53 | semidirect |
| 84. C53 | #13725 | semidirect |
| 98. C32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1696 | 2 |
| C2×#16810458 | 2 |
| #20276963 | 2 |
| C32×Dic53 | 2 |
| C2×C53×D32 | 2 |
| #13725 | 53 |