Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22⋊C16×D53 | C2 | semidirect |
| 3. #20274430 | C2 | semidirect |
| 4. #20272728 | C2 | semidirect |
| 5. #20272726 | C2 | semidirect |
| 6. #20272724 | C2 | semidirect |
| 7. C53×#1347 | C2 | semidirect |
| 8. C2×#13133236 | C4 | semidirect |
| 13. #16810865 | C4 | semidirect |
| 15. #16810856 | C4 | semidirect |
| 18. #16810660 | C4 | semidirect |
| 191. #1347 | D53 | semidirect |
| 219. C53 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284294 | 2 |
| C22⋊C16×D53 | 2 |
| #20274430 | 2 |
| #20272728 | 2 |
| #20272726 | 2 |
| #20272724 | 2 |
| C53×#1347 | 2 |
| #11703 | 53 |