Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20273474 | C2 | semidirect |
| 3. #20272677 | C2 | semidirect |
| 4. C53×#2162 | C2 | semidirect |
| 15. #16810376 | C22 | semidirect |
| 19. C4×C16×C53 | C22 | semidirect |
| 77. D424 | M16 | semidirect |
| 127. #2162 | D53 | semidirect |
| 147. C4×C16 | C2×D53 | semidirect |
| 150. C53 | #11657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D424 | 2 |
| #20273474 | 2 |
| #20272677 | 2 |
| C53×#2162 | 2 |
| #11657 | 53 |