Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20274116 | C2 | semidirect |
| 4. #20272764 | C2 | semidirect |
| 5. #20272695 | C2 | semidirect |
| 7. C53×#2241 | C2 | semidirect |
| 122. #2241 | D53 | semidirect |
| 149. C53 | #12387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287705 | 2 |
| #20276859 | 2 |
| #20274116 | 2 |
| #20272764 | 2 |
| #20272695 | 2 |
| #20272677 | 2 |
| C53×#2241 | 2 |
| #12387 | 53 |