Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #20289659 | C2 | semidirect |
| 4. #20289642 | C2 | semidirect |
| 219. C53 | #11543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289960 | 2 |
| C2×#16811466 | 2 |
| #20289659 | 2 |
| #20289642 | 2 |
| #20278996 | 2 |
| #11543 | 53 |