Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16810778 | C2 | semidirect |
| 3. #20275701 | C2 | semidirect |
| 4. #20274651 | C2 | semidirect |
| 6. #20272562 | C2 | semidirect |
| 261. C53 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810778 | 2 |
| #20278374 | 2 |
| #20275701 | 2 |
| #20274651 | 2 |
| #20273283 | 2 |
| #20272562 | 2 |
| C53×#3187 | 2 |
| #9956 | 53 |