Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20276487 | C2 | semidirect |
| 3. C2×#16810446 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#1384 | C2 | semidirect |
| 21. #16810406 | C4 | semidirect |
| 42. #13133157 | C2×C4 | semidirect |
| 56. C2×C16×C53 | C2×C4 | semidirect |
| 154. #1384 | D53 | semidirect |
| 178. C53 | #12934 | semidirect |
| 202. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283307 | 2 |
| #20276487 | 2 |
| C2×#16810446 | 2 |
| #20276342 | 2 |
| #20274766 | 2 |
| #20272820 | 2 |
| C53×#1384 | 2 |
| #12934 | 53 |