Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20273601 | C2 | semidirect |
| 3. C8×D424 | C2 | semidirect |
| 4. #20272787 | C2 | semidirect |
| 5. #20272677 | C2 | semidirect |
| 6. #20272677 | C2 | semidirect |
| 7. C53×#1312 | C2 | semidirect |
| 63. D424 | M16 | semidirect |
| 87. C8×C53 | D16 | semidirect |
| 113. #1312 | D53 | semidirect |
| 134. C53 | #12069 | semidirect |
| 201. C8 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D848 | 2 |
| #20273601 | 2 |
| C8×D424 | 2 |
| #20272787 | 2 |
| #20272677 | 2 |
| C53×#1312 | 2 |
| #12069 | 53 |