Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×C32×D53 | C2 | semidirect |
| 3. #20272852 | C2 | semidirect |
| 4. C4×#13133123 | C2 | semidirect |
| 5. C53×C4⋊C32 | C2 | semidirect |
| 23. #13133123 | D4 | semidirect |
| 47. D212 | C32 | semidirect |
| 58. C2×D53 | C2×C32 | semidirect |
| 60. C4×C53 | C2×C32 | semidirect |
| 66. C4⋊C32 | D53 | semidirect |
| 82. C53 | D4×C32 | semidirect |
| 128. C4 | C32×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D53 | 2 |
| C16×D212 | 2 |
| #20272852 | 2 |
| C4×#13133123 | 2 |
| C53×C4⋊C32 | 2 |
| D4×C32 | 53 |