Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20275552 | C2 | semidirect |
| 3. #20275550 | C2 | semidirect |
| 4. #20275143 | C2 | semidirect |
| 5. #20274893 | C2 | semidirect |
| 6. #20272582 | C2 | semidirect |
| 7. C53×#1893 | C2 | semidirect |
| 138. C22⋊Dic53 | D8 | semidirect |
| 263. #1893 | D53 | semidirect |
| 300. C53 | #10564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| #20275552 | 2 |
| #20275550 | 2 |
| #20275143 | 2 |
| #20274893 | 2 |
| #20272582 | 2 |
| C53×#1893 | 2 |
| #10564 | 53 |