Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
818 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20289813 | C2 | direct (N × H) |
| 7. C2×#13133278 | C4 | semidirect |
| 23. #13133278 | C2×C4 | semidirect |
| 170. C2×C53 | #1394 | semidirect |
| 186. C53 | C2×#1394 | semidirect |
| 337. C2 | #20289813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133278 | 2 |
| #20289813 | 2 |
| C2×#16810528 | 2 |
| C2×#1394 | 53 |