Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #20272822 | C2 | semidirect |
| 5. #20272816 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#3163 | C2 | semidirect |
| 30. C2×Dic212 | Q8 | semidirect |
| 32. C2×D424 | Q8 | semidirect |
| 152. #3163 | D53 | semidirect |
| 181. C53 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276450 | 2 |
| C2×#16810432 | 2 |
| #20275613 | 2 |
| #20272822 | 2 |
| #20272816 | 2 |
| #20272801 | 2 |
| C53×#3163 | 2 |
| #13374 | 53 |