Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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×#16810463 | C2 | semidirect |
| 2. C2×#16810461 | C2 | semidirect |
| 3. #20276806 | C2 | semidirect |
| 4. #20272896 | C2 | semidirect |
| 5. #20272893 | C2 | semidirect |
| 6. C22⋊#13133123 | C2 | semidirect |
| 133. C53 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| C2×#16810461 | 2 |
| #20276806 | 2 |
| #20272896 | 2 |
| #20272893 | 2 |
| C22⋊#13133123 | 2 |
| C2×C53×#508 | 2 |
| #13666 | 53 |