Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20276324 | C2 | semidirect |
| 3. C22⋊C16×D53 | C2 | semidirect |
| 4. #20272639 | C2 | semidirect |
| 5. #20272638 | C2 | semidirect |
| 6. #20272638 | C2 | semidirect |
| 7. C53×#1314 | C2 | semidirect |
| 216. #1314 | D53 | semidirect |
| 245. C53 | #11419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810588 | 2 |
| #20276324 | 2 |
| C22⋊C16×D53 | 2 |
| #20272639 | 2 |
| #20272638 | 2 |
| C53×#1314 | 2 |
| #11419 | 53 |