Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 3. #20272791 | C2 | semidirect |
| 4. #20272776 | C2 | semidirect |
| 5. C53×#2253 | C2 | semidirect |
| 68. #2253 | D53 | semidirect |
| 87. C53 | #12464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276888 | 2 |
| #20276553 | 2 |
| #20272791 | 2 |
| #20272776 | 2 |
| C53×#2253 | 2 |
| #12464 | 53 |