Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20276952 | C2 | semidirect |
| 3. #20276852 | C2 | semidirect |
| 4. #20274239 | C2 | semidirect |
| 5. #20272757 | C2 | semidirect |
| 6. #20272674 | C2 | semidirect |
| 7. C53×#1333 | C2 | semidirect |
| 10. #16811028 | C22 | semidirect |
| 19. C4⋊#11719908 | C22 | semidirect |
| 25. C53×#346 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 164. #1333 | D53 | semidirect |
| 188. #346 | C2×D53 | semidirect |
| 189. #334 | C2×D53 | semidirect |
| 191. C53 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286325 | 2 |
| #20276952 | 2 |
| #20276852 | 2 |
| #20274239 | 2 |
| #20272757 | 2 |
| #20272674 | 2 |
| C53×#1333 | 2 |
| #12376 | 53 |