Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276244 | C2 | semidirect |
| 3. #20276119 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 5. #20272535 | C2 | semidirect |
| 6. #20272535 | C2 | semidirect |
| 7. C53×#2072 | C2 | semidirect |
| 208. #2072 | D53 | semidirect |
| 241. C53 | #7796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281741 | 2 |
| #20276244 | 2 |
| #20276119 | 2 |
| #20272541 | 2 |
| #20272535 | 2 |
| C53×#2072 | 2 |
| #7796 | 53 |