Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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. C2×#16811000 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. #20274329 | C2 | direct (N × H) |
| 4. C2×C8×#88322 | C2 | semidirect |
| 5. C2×C53×#493 | C2 | semidirect |
| 10. #16811000 | C22 | semidirect |
| 12. #16810999 | C22 | semidirect |
| 14. C8×#88322 | C22 | semidirect |
| 18. C53×#493 | C22 | semidirect |
| 60. C2×C8×C53 | D8 | semidirect |
| 66. C2×#88322 | D8 | semidirect |
| 90. C8×C53 | C2×D8 | semidirect |
| 91. #88322 | C2×D8 | semidirect |
| 108. C2×#493 | D53 | semidirect |
| 112. C2×C53 | #1712 | semidirect |
| 126. #493 | C2×D53 | semidirect |
| 130. C53 | C2×#1712 | semidirect |
| 175. C2×C8 | #11719922 | semidirect |
| 202. C8 | C2×#11719922 | semidirect |
| 218. C2 | #20274329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810999 | 2 |
| #20274329 | 2 |
| C2×C8×#88322 | 2 |
| C2×C53×#493 | 2 |
| C2×#1712 | 53 |