Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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. #20283195 | C2 | semidirect |
| 3. #20275264 | C2 | semidirect |
| 4. #20275130 | C2 | semidirect |
| 5. #20274827 | C2 | semidirect |
| 6. #20274639 | C2 | semidirect |
| 7. C53×#1784 | C2 | semidirect |
| 189. #1784 | D53 | semidirect |
| 217. C53 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288366 | 2 |
| #20283195 | 2 |
| #20275264 | 2 |
| #20275130 | 2 |
| #20274827 | 2 |
| #20274639 | 2 |
| C53×#1784 | 2 |
| #21780 | 53 |