Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1264 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1264 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16810941 | C2 | semidirect |
| 3. #20273751 | C2 | direct (N × H) |
| 4. C2×#16810356 | C2 | semidirect |
| 5. C2×#16810349 | C2 | semidirect |
| 6. C2×C53×#400 | C2 | semidirect |
| 16. #16810941 | C22 | semidirect |
| 20. #16810356 | C22 | semidirect |
| 21. #16810349 | C22 | semidirect |
| 25. C53×#400 | C22 | semidirect |
| 203. C2×#400 | D53 | semidirect |
| 210. C2×C53 | #1616 | semidirect |
| 231. #400 | C2×D53 | semidirect |
| 237. C53 | C2×#1616 | semidirect |
| 413. C2 | #20273751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811204 | 2 |
| C2×#16810941 | 2 |
| #20273751 | 2 |
| C2×#16810356 | 2 |
| C2×#16810349 | 2 |
| C2×C53×#400 | 2 |
| C2×#1616 | 53 |