Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
346 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20286116 | C2 | semidirect |
| 2. #20276666 | C2 | semidirect |
| 4. #20272708 | C2 | semidirect |
| 5. #20272705 | C2 | semidirect |
| 6. #20272666 | C2 | semidirect |
| 7. C53×#2050 | C2 | semidirect |
| 169. #2050 | D53 | semidirect |
| 197. C53 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286116 | 2 |
| #20276666 | 2 |
| #20276661 | 2 |
| #20272708 | 2 |
| #20272705 | 2 |
| #20272666 | 2 |
| C53×#2050 | 2 |
| #12175 | 53 |