Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16811066 | C2 | semidirect |
| 2. C2×#16811063 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20275584 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 47. C2×Dic212 | D4 | semidirect |
| 67. #13133157 | D4 | semidirect |
| 84. M32×C53 | D4 | semidirect |
| 219. C2×#360 | D53 | semidirect |
| 253. C53 | #13342 | semidirect |
| 300. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| C2×#16811063 | 2 |
| #20285158 | 2 |
| C2×#16810432 | 2 |
| #20275584 | 2 |
| #20272798 | 2 |
| C2×C53×#360 | 2 |
| #13342 | 53 |