Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20285101 | C2 | semidirect |
| 2. #20284814 | C2 | semidirect |
| 3. #20273339 | C2 | semidirect |
| 4. #20273265 | C2 | semidirect |
| 5. #20273158 | C2 | semidirect |
| 6. #20272579 | C2 | semidirect |
| 35. #13133217 | D4 | semidirect |
| 36. #13133217 | D4 | semidirect |
| 56. #13133128 | D4 | semidirect |
| 57. C4×#88322 | D4 | semidirect |
| 243. C53 | #10022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285101 | 2 |
| #20284814 | 2 |
| #20273339 | 2 |
| #20273265 | 2 |
| #20273158 | 2 |
| #20272579 | 2 |
| C53×#2631 | 2 |
| #10022 | 53 |