Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 442 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. #20276462 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20276451 | C2 | semidirect |
| 5. #20275466 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#2148 | C2 | semidirect |
| 56. #13133149 | D4 | semidirect |
| 188. #2148 | D53 | semidirect |
| 220. C53 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285158 | 2 |
| #20276462 | 2 |
| #20276452 | 2 |
| #20276451 | 2 |
| #20275466 | 2 |
| #20272794 | 2 |
| C53×#2148 | 2 |
| #13416 | 53 |