Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 382 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. #20290936 | C2 | semidirect |
| 4. C2×#16811516 | C2 | semidirect |
| 5. #20289765 | C2 | semidirect |
| 6. #20289763 | C2 | semidirect |
| 9. #16811681 | C4 | semidirect |
| 15. #16811521 | C4 | semidirect |
| 167. C53 | #12618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| #20290957 | 2 |
| #20290936 | 2 |
| C2×#16811516 | 2 |
| #20289765 | 2 |
| #20289763 | 2 |
| #20274562 | 2 |
| #12618 | 53 |