Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290017 | C2 | semidirect |
| 4. #20289958 | C2 | semidirect |
| 5. #20289555 | C2 | semidirect |
| 6. #20289541 | C2 | semidirect |
| 74. C2×Q8×C53 | M16 | semidirect |
| 115. C2×#88322 | M16 | semidirect |
| 211. C53 | #9091 | semidirect |
| 259. C2×Q8 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291580 | 2 |
| #20290017 | 2 |
| #20290016 | 2 |
| #20289958 | 2 |
| #20289555 | 2 |
| #20289541 | 2 |
| C2×#16810726 | 2 |
| #9091 | 53 |