Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
332 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20291052 | C2 | semidirect |
| 4. C2×C4×#11719910 | C2 | semidirect |
| 5. #20289770 | C2 | semidirect |
| 6. #20289759 | C2 | semidirect |
| 161. C53 | #13124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291052 | 2 |
| C2×#16811521 | 2 |
| #20290945 | 2 |
| C2×C4×#11719910 | 2 |
| #20289770 | 2 |
| #20289759 | 2 |
| #20274553 | 2 |
| #13124 | 53 |