Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 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. #20276954 | C2 | semidirect |
| 3. #20276849 | C2 | semidirect |
| 4. #20272757 | C2 | semidirect |
| 5. #20272697 | C2 | semidirect |
| 6. #20272681 | C2 | semidirect |
| 7. C53×#1696 | C2 | semidirect |
| 145. #1696 | D53 | semidirect |
| 173. C53 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287805 | 2 |
| #20276954 | 2 |
| #20276849 | 2 |
| #20272757 | 2 |
| #20272697 | 2 |
| #20272681 | 2 |
| C53×#1696 | 2 |
| #12388 | 53 |