Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 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. #20276954 | C2 | semidirect |
| 3. #20274225 | C2 | semidirect |
| 4. #20272759 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#2226 | C2 | semidirect |
| 19. #16810399 | C22 | semidirect |
| 20. #16810374 | C22 | semidirect |
| 22. C53×#500 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 79. D8×C53 | SD16 | semidirect |
| 163. #2226 | D53 | semidirect |
| 176. #500 | C2×D53 | semidirect |
| 186. C4⋊C16 | C2×D53 | semidirect |
| 193. C53 | #12378 | semidirect |
| 253. D8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286325 | 2 |
| #20276954 | 2 |
| #20274225 | 2 |
| #20272759 | 2 |
| #20272682 | 2 |
| #20272672 | 2 |
| C53×#2226 | 2 |
| #12378 | 53 |