Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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. #20290938 | C2 | semidirect |
| 4. C2×#16811516 | C2 | semidirect |
| 5. #20289766 | C2 | semidirect |
| 6. #20289763 | C2 | semidirect |
| 9. #16811682 | C4 | semidirect |
| 15. #16811522 | 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 |
|---|---|
| #20291684 | 2 |
| #20290959 | 2 |
| #20290938 | 2 |
| C2×#16811516 | 2 |
| #20289766 | 2 |
| #20289763 | 2 |
| #20274558 | 2 |
| #12618 | 53 |