Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 2. #20276932 | C2 | semidirect |
| 3. #20276883 | C2 | semidirect |
| 4. #20276793 | C2 | semidirect |
| 6. #20276604 | C2 | semidirect |
| 7. #20276527 | C2 | semidirect |
| 8. C53×#3185 | C2 | semidirect |
| 18. #16810445 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810439 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 25. C53×#498 | C22 | semidirect |
| 26. C53×#494 | C22 | semidirect |
| 31. C53×#441 | C22 | semidirect |
| 158. #3185 | D53 | semidirect |
| 174. #498 | C2×D53 | semidirect |
| 175. #494 | C2×D53 | semidirect |
| 184. #441 | C2×D53 | semidirect |
| 194. C53 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283626 | 2 |
| #20276932 | 2 |
| #20276883 | 2 |
| #20276793 | 2 |
| #20276665 | 2 |
| #20276604 | 2 |
| #20276527 | 2 |
| C53×#3185 | 2 |
| #33689 | 53 |