Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 2. #20284646 | C2 | semidirect |
| 3. #20275932 | C2 | semidirect |
| 4. #20275163 | C2 | semidirect |
| 5. #20274929 | C2 | semidirect |
| 6. #20274673 | C2 | semidirect |
| 7. #20274639 | C2 | semidirect |
| 8. C53×#2310 | C2 | semidirect |
| 201. #2310 | D53 | semidirect |
| 237. C53 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288366 | 2 |
| #20284646 | 2 |
| #20275932 | 2 |
| #20275163 | 2 |
| #20274929 | 2 |
| #20274673 | 2 |
| #20274639 | 2 |
| C53×#2310 | 2 |
| #24023 | 53 |