Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20283568 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20276432 | C2 | semidirect |
| 5. #20275625 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C53×#1379 | C2 | semidirect |
| 13. C2×D848 | C4 | semidirect |
| 37. C2×D424 | C2×C4 | semidirect |
| 61. C2×C16×C53 | C2×C4 | semidirect |
| 166. #1379 | D53 | semidirect |
| 191. C53 | #13017 | semidirect |
| 220. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| #20283568 | 2 |
| C2×#16810437 | 2 |
| #20276432 | 2 |
| #20275625 | 2 |
| #20272811 | 2 |
| C53×#1379 | 2 |
| #13017 | 53 |