Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20272598 | C2 | semidirect |
| 4. #20272556 | C2 | semidirect |
| 5. C53×#2551 | C2 | semidirect |
| 23. #13133214 | Q8 | semidirect |
| 132. #2551 | D53 | semidirect |
| 154. C53 | #10348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275642 | 2 |
| #20275520 | 2 |
| #20272598 | 2 |
| #20272556 | 2 |
| C53×#2551 | 2 |
| #10348 | 53 |