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×#16811667 | C2 | semidirect |
| 2. #20291116 | C2 | direct (N × H) |
| 3. C2×#16811551 | C2 | semidirect |
| 4. C2×#16811538 | C2 | semidirect |
| 5. C2×C16×#6157 | C2 | semidirect |
| 10. #16811667 | C22 | semidirect |
| 14. #16811551 | C22 | semidirect |
| 15. #16811538 | C22 | semidirect |
| 16. C16×#6157 | C22 | semidirect |
| 18. #16811056 | C4 | semidirect |
| 20. C2×#13133160 | C4 | semidirect |
| 21. C2×D848 | C4 | semidirect |
| 23. C2×Q32×C53 | C4 | semidirect |
| 47. #13133160 | C2×C4 | semidirect |
| 48. D848 | C2×C4 | semidirect |
| 53. Q32×C53 | C2×C4 | semidirect |
| 136. C2×C53 | #2178 | semidirect |
| 145. C2×Q32 | #6157 | semidirect |
| 158. C53 | C2×#2178 | semidirect |
| 175. Q32 | C2×#6157 | semidirect |
| 267. C2 | #20291116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811667 | 2 |
| #20291116 | 2 |
| C2×#16811551 | 2 |
| C2×#16811538 | 2 |
| C2×C16×#6157 | 2 |
| C2×#16811056 | 2 |
| C2×#2178 | 53 |