Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 2. #20290916 | C2 | semidirect |
| 3. C4×#13133288 | C2 | semidirect |
| 4. #20289776 | C2 | semidirect |
| 9. #16811538 | C4 | semidirect |
| 26. D53⋊C16 | C2×C4 | semidirect |
| 29. #13133288 | C2×C4 | semidirect |
| 177. C53 | #12640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811538 | 2 |
| #20290916 | 2 |
| C4×#13133288 | 2 |
| #20289776 | 2 |
| C4×#13133240 | 2 |
| #12640 | 53 |