Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 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. #20291050 | C2 | semidirect |
| 4. C2×#16811511 | C2 | semidirect |
| 5. #20289769 | C2 | semidirect |
| 6. #20289759 | C2 | semidirect |
| 161. C53 | #13125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291050 | 2 |
| C2×#16811522 | 2 |
| #20290947 | 2 |
| C2×#16811511 | 2 |
| #20289769 | 2 |
| #20289759 | 2 |
| #20274549 | 2 |
| #13125 | 53 |