Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20272788 | C2 | semidirect |
| 5. #20272787 | C2 | semidirect |
| 6. #20272786 | C2 | semidirect |
| 7. C53×#1372 | C2 | semidirect |
| 28. #13133156 | C8 | semidirect |
| 64. C16×C53 | C2×C8 | semidirect |
| 66. #11719908 | C2×C8 | semidirect |
| 105. #1372 | D53 | semidirect |
| 127. C53 | #12009 | semidirect |
| 171. C16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133156 | 2 |
| #20273462 | 2 |
| #335×D53 | 2 |
| #20272788 | 2 |
| #20272787 | 2 |
| #20272786 | 2 |
| C53×#1372 | 2 |
| #12009 | 53 |