Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 124 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. #20289931 | C2 | semidirect |
| 4. #20289911 | C2 | semidirect |
| 5. #20289547 | C2 | semidirect |
| 6. #20289546 | C2 | semidirect |
| 196. C53 | #8186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133304 | 2 |
| #20290007 | 2 |
| #20289931 | 2 |
| #20289911 | 2 |
| #20289547 | 2 |
| #20289546 | 2 |
| #20273094 | 2 |
| #8186 | 53 |