Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #20276951 | C2 | semidirect |
| 3. #20276863 | C2 | semidirect |
| 4. #20274229 | C2 | semidirect |
| 5. #20272681 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 10. #16811028 | C22 | semidirect |
| 22. #16810399 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 101. D424 | SD16 | semidirect |
| 165. #1360 | D53 | semidirect |
| 186. C4⋊C16 | C2×D53 | semidirect |
| 191. #334 | C2×D53 | semidirect |
| 193. C53 | #12378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286324 | 2 |
| #20276951 | 2 |
| #20276863 | 2 |
| #20274229 | 2 |
| #20272681 | 2 |
| #20272672 | 2 |
| C53×#1360 | 2 |
| #12378 | 53 |