Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20274510 | C2 | semidirect |
| 3. #20273057 | C2 | semidirect |
| 4. #20272722 | C2 | semidirect |
| 5. #20272720 | C2 | semidirect |
| 216. C53 | #11778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279619 | 2 |
| #20274510 | 2 |
| #20273057 | 2 |
| #20272722 | 2 |
| #20272720 | 2 |
| #20272718 | 2 |
| C53×#1345 | 2 |
| #11778 | 53 |