Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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. #349×D53 | C2 | semidirect |
| 3. H(3,ℤ/4)×D53 | C2 | semidirect |
| 4. #20272704 | C2 | semidirect |
| 5. #20272702 | C2 | semidirect |
| 6. #20272700 | C2 | semidirect |
| 7. C53×#1339 | C2 | semidirect |
| 8. C2×#13133236 | C4 | semidirect |
| 13. #16810882 | C4 | semidirect |
| 15. #16810873 | C4 | semidirect |
| 18. #16810658 | C4 | semidirect |
| 31. C2×Dic212 | C2×C4 | semidirect |
| 59. #13133149 | C2×C4 | semidirect |
| 63. C2×D8×C53 | C2×C4 | semidirect |
| 68. #106×C53 | C2×C4 | semidirect |
| 204. #1339 | D53 | semidirect |
| 231. C53 | #11685 | semidirect |
| 238. C2×D8 | C4×D53 | semidirect |
| 270. #106 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284322 | 2 |
| #349×D53 | 2 |
| H(3,ℤ/4)×D53 | 2 |
| #20272704 | 2 |
| #20272702 | 2 |
| #20272700 | 2 |
| C53×#1339 | 2 |
| #11685 | 53 |