Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20289688 | C2 | semidirect |
| 4. #20289687 | C2 | semidirect |
| 12. C2×Q16×D53 | C4 | semidirect |
| 16. #16810881 | C4 | semidirect |
| 20. #16810658 | C4 | semidirect |
| 22. C53×#470 | C4 | semidirect |
| 178. #470 | #6157 | semidirect |
| 188. C53 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290953 | 2 |
| #20290598 | 2 |
| #20289688 | 2 |
| #20289687 | 2 |
| #20284368 | 2 |
| #11869 | 53 |