Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1382 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1382 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 |
|---|---|---|
| 2. C22×#13133136 | C2 | semidirect |
| 3. C2×#16810419 | C2 | direct (N × H) |
| 4. C22×#101×C53 | C2 | semidirect |
| 15. C2×#13133136 | C22 | semidirect |
| 16. #16810419 | C22 | direct (N × H) |
| 20. C2×#101×C53 | C22 | semidirect |
| 42. #13133136 | C23 | semidirect |
| 56. #101×C53 | C23 | semidirect |
| 149. C22×C53 | #355 | semidirect |
| 166. C22×#101 | D53 | semidirect |
| 170. C2×C53 | C2×#355 | semidirect |
| 187. C2×#101 | C2×D53 | semidirect |
| 189. C53 | C22×#355 | semidirect |
| 225. #101 | C22×D53 | semidirect |
| 321. C22 | #16810419 | direct (N × H) |
| 335. C2 | C2×#16810419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133206 | 2 |
| C22×#13133136 | 2 |
| C2×#16810419 | 2 |
| C22×#101×C53 | 2 |
| C22×#355 | 53 |