Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16811064 | C2 | semidirect |
| 3. C2×#16810878 | C2 | semidirect |
| 4. C2×#16810434 | C2 | semidirect |
| 5. C2×#16810404 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 60. #13133157 | D4 | semidirect |
| 63. #13133149 | D4 | semidirect |
| 73. C2×Q16×C53 | D4 | semidirect |
| 210. #2141 | D53 | semidirect |
| 242. C53 | #13317 | semidirect |
| 256. C2×Q16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20284325 | 2 |
| C2×#16810878 | 2 |
| C2×#16810434 | 2 |
| C2×#16810404 | 2 |
| #20272820 | 2 |
| C53×#2141 | 2 |
| #13317 | 53 |