Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16811064 | C2 | semidirect |
| 3. #20285204 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20275611 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 210. #2141 | D53 | semidirect |
| 244. C53 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| C2×#16811064 | 2 |
| #20285204 | 2 |
| #20276450 | 2 |
| #20275611 | 2 |
| #20272800 | 2 |
| C53×#2141 | 2 |
| #13335 | 53 |