Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20287320 | C2 | semidirect |
| 2. #20276957 | C2 | semidirect |
| 3. #20276751 | C2 | semidirect |
| 4. #20274194 | C2 | semidirect |
| 5. #20272766 | C2 | semidirect |
| 6. #20272683 | C2 | semidirect |
| 7. C53×#1330 | C2 | semidirect |
| 153. #1330 | D53 | semidirect |
| 179. C53 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287320 | 2 |
| #20276957 | 2 |
| #20276751 | 2 |
| #20274194 | 2 |
| #20272766 | 2 |
| #20272683 | 2 |
| C53×#1330 | 2 |
| #12348 | 53 |