Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 314 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. #20287322 | C2 | semidirect |
| 2. #20276956 | C2 | semidirect |
| 3. #20274191 | C2 | semidirect |
| 4. #20272766 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#2206 | C2 | semidirect |
| 149. #2206 | 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 |
|---|---|
| #20287322 | 2 |
| #20276956 | 2 |
| #20274191 | 2 |
| #20272766 | 2 |
| #20272682 | 2 |
| #20272672 | 2 |
| C53×#2206 | 2 |
| #12348 | 53 |