Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. C2×#16810400 | C2 | semidirect |
| 5. #20275451 | C2 | semidirect |
| 6. #20272825 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 16. #16810428 | C4 | semidirect |
| 17. #16810425 | C4 | semidirect |
| 149. #1383 | D53 | semidirect |
| 171. C53 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810432 | 2 |
| #20276428 | 2 |
| C2×#16810400 | 2 |
| #20275606 | 2 |
| #20275451 | 2 |
| #20272825 | 2 |
| C53×#1383 | 2 |
| #13153 | 53 |