Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16810993 | C2 | semidirect |
| 3. C2×#16810983 | C2 | semidirect |
| 4. #20274039 | C2 | direct (N × H) |
| 5. C2×#16810362 | C2 | semidirect |
| 6. C2×C53×#330 | C2 | semidirect |
| 16. #16810993 | C22 | semidirect |
| 18. #16810983 | C22 | semidirect |
| 23. #16810362 | C22 | semidirect |
| 26. C53×#330 | C22 | semidirect |
| 149. C2×#330 | D53 | semidirect |
| 151. C2×C53 | #1662 | semidirect |
| 173. #330 | C2×D53 | semidirect |
| 175. C53 | C2×#1662 | semidirect |
| 294. C2 | #20274039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811371 | 2 |
| C2×#16810993 | 2 |
| C2×#16810983 | 2 |
| #20274039 | 2 |
| C2×#16810362 | 2 |
| C2×C53×#330 | 2 |
| C2×#1662 | 53 |