Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 4. #20272637 | C2 | semidirect |
| 5. #20272636 | C2 | semidirect |
| 6. #20272635 | C2 | semidirect |
| 7. C53×#1313 | C2 | semidirect |
| 28. C16×D53 | C8 | semidirect |
| 53. C16×C53 | C2×C8 | semidirect |
| 55. #11719908 | C2×C8 | semidirect |
| 85. #1313 | D53 | direct (N × H) |
| 88. D53 | #1313 | direct (N × H) |
| 102. C53 | C2×#1313 | semidirect |
| 137. C16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D53 | 2 |
| #322×D53 | 2 |
| #20272637 | 2 |
| #20272636 | 2 |
| #20272635 | 2 |
| C53×#1313 | 2 |
| C2×#1313 | 53 |