Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1154 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20283326 | C2 | semidirect |
| 3. #20276465 | C2 | semidirect |
| 4. C2×#16810437 | C2 | semidirect |
| 5. C53×#3407 | C2 | semidirect |
| 14. C2×#13133153 | C22 | semidirect |
| 15. #16810440 | C22 | semidirect |
| 16. #16810437 | C22 | semidirect |
| 19. C2×M32×C53 | C22 | semidirect |
| 113. #3407 | D53 | semidirect |
| 130. C2×M32 | C2×D53 | semidirect |
| 135. C53 | #33392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811428 | 2 |
| #20283326 | 2 |
| #20276465 | 2 |
| C2×#16810437 | 2 |
| C53×#3407 | 2 |
| #33392 | 53 |