Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20287851 | C2 | semidirect |
| 2. C2×#16811059 | C2 | semidirect |
| 3. #20285196 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20275611 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 7. C53×#2140 | C2 | semidirect |
| 46. C2×Dic212 | D4 | semidirect |
| 51. C2×D424 | D4 | semidirect |
| 66. #13133157 | D4 | semidirect |
| 83. C2×C16×C53 | D4 | semidirect |
| 215. #2140 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
| 297. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| C2×#16811059 | 2 |
| #20285196 | 2 |
| #20276450 | 2 |
| #20275611 | 2 |
| #20272800 | 2 |
| C53×#2140 | 2 |
| #13334 | 53 |