Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283312 | C2 | semidirect |
| 3. C2×#16810424 | C2 | semidirect |
| 4. C2×#16810408 | C2 | semidirect |
| 5. #20272824 | C2 | semidirect |
| 6. #20272810 | C2 | semidirect |
| 7. C53×#2140 | C2 | semidirect |
| 13. #16810890 | C4 | semidirect |
| 51. #13133153 | C2×C4 | semidirect |
| 63. C2×D8×C53 | C2×C4 | semidirect |
| 184. #2140 | D53 | semidirect |
| 216. C53 | #12996 | semidirect |
| 228. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810890 | 2 |
| #20283312 | 2 |
| C2×#16810424 | 2 |
| C2×#16810408 | 2 |
| #20272824 | 2 |
| #20272810 | 2 |
| C53×#2140 | 2 |
| #12996 | 53 |