Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 94 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. #20291075 | C2 | semidirect |
| 2. #20290273 | C2 | semidirect |
| 3. #20289670 | C2 | semidirect |
| 4. #20289669 | C2 | semidirect |
| 9. #16811509 | C22 | semidirect |
| 11. #16811486 | C22 | semidirect |
| 75. D8×C53 | M16 | semidirect |
| 93. D424 | M16 | semidirect |
| 185. C53 | #11657 | semidirect |
| 239. D8 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| #20290273 | 2 |
| #20289670 | 2 |
| #20289669 | 2 |
| C4×D8×D53 | 2 |
| #11657 | 53 |