Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276509 | C2 | semidirect |
| 3. #20276462 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20276336 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C53×#1815 | C2 | semidirect |
| 176. #1815 | D53 | semidirect |
| 203. C53 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284435 | 2 |
| #20276509 | 2 |
| #20276462 | 2 |
| C2×#16810432 | 2 |
| #20276336 | 2 |
| #20272813 | 2 |
| C53×#1815 | 2 |
| #13391 | 53 |