Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276516 | C2 | semidirect |
| 3. #20273475 | C2 | semidirect |
| 4. #20272683 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272681 | C2 | semidirect |
| 7. C53×#1333 | C2 | semidirect |
| 21. #16810399 | C22 | semidirect |
| 23. #16810374 | C22 | semidirect |
| 25. C53×#346 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 166. #1333 | D53 | semidirect |
| 188. #346 | C2×D53 | semidirect |
| 191. #334 | C2×D53 | semidirect |
| 192. C53 | #11667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D53 | 2 |
| #20276516 | 2 |
| #20273475 | 2 |
| #20272683 | 2 |
| #20272682 | 2 |
| #20272681 | 2 |
| C53×#1333 | 2 |
| #11667 | 53 |