Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20284656 | C2 | semidirect |
| 3. #20284651 | C2 | semidirect |
| 4. #20274784 | C2 | semidirect |
| 5. #20273074 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#1471 | C2 | semidirect |
| 210. #1471 | D53 | semidirect |
| 245. C53 | #9977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| #20284656 | 2 |
| #20284651 | 2 |
| #20274784 | 2 |
| #20273074 | 2 |
| #20272591 | 2 |
| C53×#1471 | 2 |
| #9977 | 53 |