Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276951 | C2 | semidirect |
| 2. #20276862 | C2 | semidirect |
| 3. #20274228 | C2 | semidirect |
| 4. #20272758 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272673 | C2 | semidirect |
| 8. #16811028 | C22 | semidirect |
| 11. C4⋊#11719908 | C22 | semidirect |
| 15. #16810399 | C22 | semidirect |
| 16. #16810374 | C22 | semidirect |
| 85. D8×C53 | SD16 | semidirect |
| 193. C53 | #12378 | semidirect |
| 253. D8 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276951 | 2 |
| #20276862 | 2 |
| #20274228 | 2 |
| #20272758 | 2 |
| #20272682 | 2 |
| #20272673 | 2 |
| C53×#3273 | 2 |
| #12378 | 53 |