Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 184 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×#16811665 | C2 | semidirect |
| 2. #20291114 | C2 | direct (N × H) |
| 3. C2×#16811551 | C2 | semidirect |
| 4. C2×#16811537 | C2 | semidirect |
| 5. C2×C16×#6157 | C2 | semidirect |
| 10. #16811665 | C22 | semidirect |
| 14. #16811551 | C22 | semidirect |
| 15. #16811537 | C22 | semidirect |
| 16. C16×#6157 | C22 | semidirect |
| 18. #16811052 | C4 | semidirect |
| 20. C2×Dic424 | C4 | semidirect |
| 21. C2×#13133161 | C4 | semidirect |
| 23. C2×D16×C53 | C4 | semidirect |
| 47. Dic424 | C2×C4 | semidirect |
| 48. #13133161 | C2×C4 | semidirect |
| 53. D16×C53 | C2×C4 | semidirect |
| 137. C2×C53 | #2178 | semidirect |
| 147. C2×D16 | #6157 | semidirect |
| 158. C53 | C2×#2178 | semidirect |
| 177. D16 | C2×#6157 | semidirect |
| 267. C2 | #20291114 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811665 | 2 |
| #20291114 | 2 |
| C2×#16811551 | 2 |
| C2×#16811537 | 2 |
| C2×C16×#6157 | 2 |
| C2×#16811052 | 2 |
| C2×#2178 | 53 |