Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275668 | C2 | semidirect |
| 3. #20273441 | C2 | semidirect |
| 5. #20272584 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 26. C53×#501 | C4 | semidirect |
| 27. C53×#489 | C4 | semidirect |
| 198. #501 | Dic53 | semidirect |
| 199. #489 | Dic53 | semidirect |
| 221. C53 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283854 | 2 |
| #20275668 | 2 |
| #20273441 | 2 |
| #20273240 | 2 |
| #20272584 | 2 |
| #20272570 | 2 |
| C53×#3238 | 2 |
| #9375 | 53 |