Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20274703 | C2 | semidirect |
| 3. #20274647 | C2 | semidirect |
| 4. #20272583 | C2 | semidirect |
| 5. C53×#2973 | C2 | semidirect |
| 11. #16810540 | C4 | semidirect |
| 12. #16810532 | C4 | semidirect |
| 47. C22×C8×C53 | D4 | semidirect |
| 204. #2973 | D53 | semidirect |
| 235. C53 | #9472 | semidirect |
| 247. C22×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278071 | 2 |
| #20274703 | 2 |
| #20274647 | 2 |
| #20272583 | 2 |
| C53×#2973 | 2 |
| #9472 | 53 |