Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274704 | C2 | semidirect |
| 3. #20273473 | C2 | semidirect |
| 4. #20273166 | C2 | semidirect |
| 5. C2×#16810350 | C2 | semidirect |
| 6. #20272590 | C2 | semidirect |
| 7. C53×#1547 | C2 | semidirect |
| 197. #1547 | D53 | semidirect |
| 229. C53 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284175 | 2 |
| #20274704 | 2 |
| #20273473 | 2 |
| #20273166 | 2 |
| C2×#16810350 | 2 |
| #20272590 | 2 |
| C53×#1547 | 2 |
| #10456 | 53 |