Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #20272788 | C2 | semidirect |
| 4. #20272679 | C2 | semidirect |
| 6. #20272633 | C2 | semidirect |
| 7. C53×#1591 | C2 | semidirect |
| 85. C8×C53 | SD32 | semidirect |
| 103. #1591 | D53 | semidirect |
| 128. C53 | #12070 | semidirect |
| 192. C8 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133160 | 2 |
| C8×D424 | 2 |
| #20272788 | 2 |
| #20272679 | 2 |
| #20272675 | 2 |
| #20272633 | 2 |
| C53×#1591 | 2 |
| #12070 | 53 |