Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #20276643 | C2 | semidirect |
| 2. #20276626 | C2 | semidirect |
| 3. #20275824 | C2 | semidirect |
| 4. #20272733 | C2 | semidirect |
| 5. #20272730 | C2 | semidirect |
| 6. #20272641 | C2 | semidirect |
| 7. C53×#3203 | C2 | semidirect |
| 178. #3203 | D53 | semidirect |
| 211. C53 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276643 | 2 |
| #20276626 | 2 |
| #20275824 | 2 |
| #20272733 | 2 |
| #20272730 | 2 |
| #20272641 | 2 |
| C53×#3203 | 2 |
| #12110 | 53 |