Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276553 | C2 | semidirect |
| 3. #20272790 | C2 | semidirect |
| 4. #20272688 | C2 | semidirect |
| 5. #20272687 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2170 | C2 | semidirect |
| 25. #13133163 | C8 | semidirect |
| 26. #13133161 | C8 | semidirect |
| 27. #13133160 | C8 | semidirect |
| 28. #13133158 | C8 | semidirect |
| 101. #2170 | D53 | semidirect |
| 125. C53 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276594 | 2 |
| #20276553 | 2 |
| #20272790 | 2 |
| #20272688 | 2 |
| #20272687 | 2 |
| C16×#88322 | 2 |
| C53×#2170 | 2 |
| #12046 | 53 |