Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1230 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 355 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×#16810702 | C2 | semidirect |
| 3. #20275509 | C2 | semidirect |
| 4. #20274867 | C2 | semidirect |
| 5. C42×C8×C53 | C2 | semidirect |
| 34. C4×C8×C53 | D4 | semidirect |
| 49. C42×C53 | M16 | semidirect |
| 72. C8×C53 | #127 | semidirect |
| 82. C4×C53 | #436 | semidirect |
| 90. C42×C8 | D53 | semidirect |
| 106. C53 | #21681 | semidirect |
| 124. C4×C8 | D212 | semidirect |
| 143. C42 | #11719912 | semidirect |
| 163. C8 | #13133214 | semidirect |
| 172. C4 | #16810702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810702 | 2 |
| C4×#13133214 | 2 |
| #20275509 | 2 |
| #20274867 | 2 |
| C42×C8×C53 | 2 |
| #21681 | 53 |