Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276319 | C2 | semidirect |
| 5. #20275493 | C2 | semidirect |
| 6. #20272831 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 15. #16810440 | C4 | semidirect |
| 16. #16810437 | C4 | semidirect |
| 141. #1386 | D53 | semidirect |
| 162. C53 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276465 | 2 |
| C2×#16810432 | 2 |
| #20276319 | 2 |
| #20275611 | 2 |
| #20275493 | 2 |
| #20272831 | 2 |
| C53×#1386 | 2 |
| #13156 | 53 |