Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16811039 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20274770 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 15. #16810895 | C4 | semidirect |
| 16. #16810890 | C4 | semidirect |
| 178. C2×#359 | D53 | semidirect |
| 209. C53 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811039 | 2 |
| #20284431 | 2 |
| #20276451 | 2 |
| #20274770 | 2 |
| #20272826 | 2 |
| #20272811 | 2 |
| C2×C53×#359 | 2 |
| #13071 | 53 |