Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20287288 | C2 | semidirect |
| 2. #20276958 | C2 | semidirect |
| 3. #20276756 | C2 | semidirect |
| 5. #20272684 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#1363 | C2 | semidirect |
| 146. #1363 | D53 | semidirect |
| 173. C53 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287288 | 2 |
| #20276958 | 2 |
| #20276756 | 2 |
| #20274195 | 2 |
| #20272684 | 2 |
| #20272672 | 2 |
| C53×#1363 | 2 |
| #12349 | 53 |