Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1254 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 3. C2×#16810421 | C2 | direct (N × H) |
| 16. #16810421 | C22 | direct (N × H) |
| 145. C22×C53 | #356 | semidirect |
| 163. C2×C53 | C2×#356 | semidirect |
| 181. C53 | C22×#356 | semidirect |
| 305. C22 | #16810421 | direct (N × H) |
| 319. C2 | C2×#16810421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133215 | 2 |
| C22×#13133136 | 2 |
| C2×#16810421 | 2 |
| C22×#101×C53 | 2 |
| C22×#356 | 53 |