Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20283626 | C2 | semidirect |
| 2. #20276927 | C2 | semidirect |
| 3. #20276883 | C2 | semidirect |
| 4. #20276788 | C2 | semidirect |
| 5. #20276660 | C2 | semidirect |
| 6. #20276611 | C2 | semidirect |
| 7. #20276527 | C2 | semidirect |
| 8. C53×#3184 | C2 | semidirect |
| 18. #16810445 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810436 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 25. C53×#498 | C22 | semidirect |
| 26. C53×#493 | C22 | semidirect |
| 31. C53×#442 | C22 | semidirect |
| 107. Dic212 | #41 | semidirect |
| 109. D424 | #41 | semidirect |
| 165. #3184 | D53 | semidirect |
| 182. #498 | C2×D53 | semidirect |
| 183. #493 | C2×D53 | semidirect |
| 192. #442 | C2×D53 | semidirect |
| 202. C53 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283626 | 2 |
| #20276927 | 2 |
| #20276883 | 2 |
| #20276788 | 2 |
| #20276660 | 2 |
| #20276611 | 2 |
| #20276527 | 2 |
| C53×#3184 | 2 |
| #33688 | 53 |