Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×D16×D53 | C2 | semidirect |
| 2. #493×D53 | C2 | semidirect |
| 3. #20276965 | C2 | semidirect |
| 4. #20276964 | C2 | semidirect |
| 5. #20276963 | C2 | semidirect |
| 6. C4×C16×D53 | C2 | semidirect |
| 7. C53×#2246 | C2 | semidirect |
| 11. C2×D848 | C22 | semidirect |
| 12. C2×#13133158 | C22 | semidirect |
| 15. #16811000 | C22 | semidirect |
| 18. #16810998 | C22 | semidirect |
| 20. C4×#11719908 | C22 | semidirect |
| 21. C16×Dic53 | C22 | semidirect |
| 22. C2×D16×C53 | C22 | semidirect |
| 23. C53×#493 | C22 | semidirect |
| 24. C4×C16×C53 | C22 | semidirect |
| 42. C16×D53 | D4 | semidirect |
| 79. C16×C53 | C2×D4 | semidirect |
| 80. #11719908 | C2×D4 | semidirect |
| 98. C4×D53 | D16 | semidirect |
| 114. C4×C53 | C2×D16 | semidirect |
| 118. Dic53 | C2×D16 | semidirect |
| 124. #2246 | D53 | direct (N × H) |
| 130. D53 | #2246 | direct (N × H) |
| 137. C2×D16 | C2×D53 | semidirect |
| 143. #493 | C2×D53 | semidirect |
| 147. C4×C16 | C2×D53 | semidirect |
| 148. C53 | C2×#2246 | semidirect |
| 204. C16 | D4×D53 | semidirect |
| 239. C4 | D16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| #493×D53 | 2 |
| #20276965 | 2 |
| #20276964 | 2 |
| #20276963 | 2 |
| C4×C16×D53 | 2 |
| C53×#2246 | 2 |
| C2×#2246 | 53 |