Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20274650 | C2 | semidirect |
| 5. #20272620 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#1784 | C2 | semidirect |
| 11. #16810779 | C4 | semidirect |
| 13. #16810762 | C4 | semidirect |
| 246. #1784 | D53 | semidirect |
| 283. C53 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283949 | 2 |
| #20283765 | 2 |
| #20274650 | 2 |
| #20273259 | 2 |
| #20272620 | 2 |
| #20272591 | 2 |
| C53×#1784 | 2 |
| #9519 | 53 |