Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16811520 | C2 | semidirect |
| 2. C2×#16811491 | C2 | semidirect |
| 3. #20289685 | C2 | direct (N × H) |
| 8. #16811520 | C22 | semidirect |
| 10. #16811491 | C22 | semidirect |
| 15. #16810873 | C4 | semidirect |
| 17. C2×#13133149 | C4 | semidirect |
| 19. C22×D8×C53 | C4 | semidirect |
| 46. #13133149 | C2×C4 | semidirect |
| 53. C2×D8×C53 | C2×C4 | semidirect |
| 177. C2×C53 | #1339 | semidirect |
| 181. C22×D8 | #6157 | semidirect |
| 196. C53 | C2×#1339 | semidirect |
| 203. C2×D8 | C2×#6157 | semidirect |
| 351. C2 | #20289685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811520 | 2 |
| C2×#16811491 | 2 |
| #20289685 | 2 |
| C2×#16810873 | 2 |
| C2×#1339 | 53 |