Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 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. C2×#16810460 | C2 | semidirect |
| 2. C2×C32×D53 | C2 | semidirect |
| 3. #20276803 | C2 | semidirect |
| 5. #20272916 | C2 | semidirect |
| 6. #20272894 | C2 | semidirect |
| 7. C53×#1416 | C2 | semidirect |
| 33. #13133123 | D4 | semidirect |
| 84. C2×D53 | SD64 | semidirect |
| 96. #1416 | D53 | semidirect |
| 116. C53 | #13696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810460 | 2 |
| C2×C32×D53 | 2 |
| #20276803 | 2 |
| #20276802 | 2 |
| #20272916 | 2 |
| #20272894 | 2 |
| C53×#1416 | 2 |
| #13696 | 53 |