Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2062 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×#13133132 | C2 | semidirect |
| 3. C2×#16810415 | C2 | direct (N × H) |
| 4. C22×#99×C53 | C2 | semidirect |
| 5. C23×D212 | C4 | semidirect |
| 10. C2×#13133213 | C4 | semidirect |
| 13. C22×C4×Dic53 | C4 | semidirect |
| 15. C2×#13133132 | C22 | semidirect |
| 16. #16810415 | C22 | direct (N × H) |
| 20. C2×#99×C53 | C22 | semidirect |
| 25. C22×D212 | C2×C4 | semidirect |
| 37. #13133213 | C2×C4 | semidirect |
| 42. C2×C4×Dic53 | C2×C4 | semidirect |
| 44. #13133132 | C23 | semidirect |
| 58. #99×C53 | C23 | semidirect |
| 111. C2×D212 | C22×C4 | semidirect |
| 117. C4×Dic53 | C22×C4 | semidirect |
| 191. C22×C53 | #353 | semidirect |
| 207. C22×#99 | D53 | semidirect |
| 215. C2×C53 | C2×#353 | semidirect |
| 232. C2×#99 | C2×D53 | semidirect |
| 234. C53 | C22×#353 | semidirect |
| 272. #99 | C22×D53 | semidirect |
| 409. C22 | #16810415 | direct (N × H) |
| 425. C2 | C2×#16810415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133213 | 2 |
| C22×#13133132 | 2 |
| C2×#16810415 | 2 |
| C22×#99×C53 | 2 |
| C22×#353 | 53 |