Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
728 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×#16811641 | C2 | semidirect |
| 2. #20290572 | C2 | semidirect |
| 3. C2×#16811481 | C2 | semidirect |
| 4. #20289593 | C2 | semidirect |
| 30. #13133284 | D4 | semidirect |
| 267. C53 | #9134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811641 | 2 |
| #20290572 | 2 |
| C2×#16811481 | 2 |
| #20289593 | 2 |
| #20283059 | 2 |
| #9134 | 53 |