Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. C22×#13133123 | C2 | semidirect |
| 3. #20272892 | C2 | direct (N × H) |
| 4. C2×C53×#366 | C2 | semidirect |
| 8. C2×D848 | C4 | semidirect |
| 11. C2×#13133123 | C22 | semidirect |
| 15. C53×#366 | C22 | semidirect |
| 23. D848 | C2×C4 | semidirect |
| 84. C2×#366 | D53 | semidirect |
| 86. C2×C53 | #1415 | semidirect |
| 101. #366 | C2×D53 | semidirect |
| 102. C53 | C2×#1415 | semidirect |
| 169. C2 | #20272892 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C22×#13133123 | 2 |
| #20272892 | 2 |
| C2×C53×#366 | 2 |
| C2×#1415 | 53 |