Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 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 |
| 2. C2×#16810895 | C2 | semidirect |
| 4. C2×#16810431 | C2 | semidirect |
| 5. C2×#16810406 | C2 | semidirect |
| 6. #20272823 | C2 | semidirect |
| 7. C2×C53×#358 | C2 | semidirect |
| 60. #13133157 | D4 | semidirect |
| 63. #13133153 | D4 | semidirect |
| 73. C2×Q16×C53 | D4 | semidirect |
| 209. C2×#358 | D53 | semidirect |
| 242. C53 | #13308 | semidirect |
| 259. 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 |
| C2×#16810895 | 2 |
| #20284387 | 2 |
| C2×#16810431 | 2 |
| C2×#16810406 | 2 |
| #20272823 | 2 |
| C2×C53×#358 | 2 |
| #13308 | 53 |