Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 2. #20276910 | C2 | semidirect |
| 3. #20276901 | C2 | semidirect |
| 4. #20276157 | C2 | semidirect |
| 5. #20272729 | C2 | semidirect |
| 6. #20272640 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 155. #1350 | D53 | semidirect |
| 183. C53 | #12285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285618 | 2 |
| #20276910 | 2 |
| #20276901 | 2 |
| #20276157 | 2 |
| #20272729 | 2 |
| #20272640 | 2 |
| C53×#1350 | 2 |
| #12285 | 53 |