Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20275109 | C2 | semidirect |
| 5. #20274932 | C2 | semidirect |
| 6. #20272841 | C2 | semidirect |
| 7. C2×C53×#356 | C2 | semidirect |
| 214. C2×#356 | D53 | semidirect |
| 247. C53 | #13427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281721 | 2 |
| C2×#16810419 | 2 |
| #20275116 | 2 |
| #20275109 | 2 |
| #20274932 | 2 |
| #20272841 | 2 |
| C2×C53×#356 | 2 |
| #13427 | 53 |