Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 492 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. #20273491 | C2 | semidirect |
| 4. #20273383 | C2 | semidirect |
| 5. #20273107 | C2 | semidirect |
| 6. #20272611 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 181. #1545 | D53 | semidirect |
| 208. C53 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810815 | 2 |
| #20274704 | 2 |
| #20273491 | 2 |
| #20273383 | 2 |
| #20273107 | 2 |
| #20272611 | 2 |
| C53×#1545 | 2 |
| #10440 | 53 |