Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16810435 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276432 | C2 | semidirect |
| 5. #20276319 | C2 | semidirect |
| 6. #20274840 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 13. #16811008 | C4 | semidirect |
| 14. #16810998 | C4 | semidirect |
| 46. #13133157 | D4 | semidirect |
| 64. C2×C16×C53 | D4 | semidirect |
| 172. #2143 | D53 | semidirect |
| 201. C53 | #13215 | semidirect |
| 235. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285202 | 2 |
| C2×#16810435 | 2 |
| #20276451 | 2 |
| #20276432 | 2 |
| #20276319 | 2 |
| #20274840 | 2 |
| C53×#2143 | 2 |
| #13215 | 53 |