Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 2. #20276529 | C2 | semidirect |
| 3. #20276318 | C2 | semidirect |
| 4. #20272750 | C2 | semidirect |
| 5. #20272747 | C2 | semidirect |
| 6. #20272747 | C2 | semidirect |
| 7. C53×#1356 | C2 | semidirect |
| 137. #1356 | D53 | semidirect |
| 163. C53 | #11912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285346 | 2 |
| #20276529 | 2 |
| #20276318 | 2 |
| #20272750 | 2 |
| #20272747 | 2 |
| C53×#1356 | 2 |
| #11912 | 53 |