Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283844 | C2 | semidirect |
| 3. #20275555 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. #20273155 | C2 | semidirect |
| 6. #20272628 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 166. Dic106 | #100 | semidirect |
| 203. #1299 | D53 | semidirect |
| 233. C53 | #9360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284196 | 2 |
| #20283844 | 2 |
| #20275555 | 2 |
| #20273382 | 2 |
| #20273155 | 2 |
| #20272628 | 2 |
| C53×#1299 | 2 |
| #9360 | 53 |