Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16811059 | C2 | semidirect |
| 2. #20284435 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. #20276442 | C2 | semidirect |
| 5. #20276336 | C2 | semidirect |
| 6. #20272828 | C2 | semidirect |
| 7. C2×C53×#472 | C2 | semidirect |
| 205. C2×#472 | D53 | semidirect |
| 240. C53 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| #20284435 | 2 |
| C2×#16810436 | 2 |
| #20276442 | 2 |
| #20276336 | 2 |
| #20272828 | 2 |
| C2×C53×#472 | 2 |
| #13323 | 53 |