Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20277313 | C2 | semidirect |
| 3. #20273284 | C2 | semidirect |
| 4. #20272583 | C2 | semidirect |
| 5. C2×C53×#323 | C2 | semidirect |
| 8. #16810548 | C4 | semidirect |
| 10. #16810532 | C4 | semidirect |
| 41. #13133124 | D4 | semidirect |
| 182. C2×#323 | D53 | semidirect |
| 208. C53 | #9205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280449 | 2 |
| #20277313 | 2 |
| #20273284 | 2 |
| #20272583 | 2 |
| C2×C53×#323 | 2 |
| #9205 | 53 |