Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20276958 | C2 | semidirect |
| 3. #20276557 | C2 | semidirect |
| 4. #20272782 | C2 | semidirect |
| 5. #20272776 | C2 | semidirect |
| 6. #20272751 | C2 | semidirect |
| 7. C53×#2231 | C2 | semidirect |
| 93. #2231 | D53 | semidirect |
| 118. C53 | #12465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276958 | 2 |
| #20276791 | 2 |
| #20276557 | 2 |
| #20272782 | 2 |
| #20272776 | 2 |
| #20272751 | 2 |
| C53×#2231 | 2 |
| #12465 | 53 |