Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×#16811058 | C2 | semidirect |
| 2. C2×#16810893 | C2 | semidirect |
| 3. C2×#16810430 | C2 | semidirect |
| 4. C2×#16810423 | C2 | semidirect |
| 5. C2×#16810407 | C2 | semidirect |
| 6. #20272823 | C2 | semidirect |
| 7. C53×#3061 | C2 | semidirect |
| 40. C2×D424 | D4 | semidirect |
| 46. #13133157 | D4 | semidirect |
| 52. #13133153 | D4 | semidirect |
| 213. #3061 | D53 | semidirect |
| 249. C53 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C2×#16810893 | 2 |
| C2×#16810430 | 2 |
| C2×#16810423 | 2 |
| C2×#16810407 | 2 |
| #20272823 | 2 |
| C53×#3061 | 2 |
| #13307 | 53 |