Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16814667 | C2 | semidirect |
| 2. C2×#16814665 | C2 | semidirect |
| 3. #20301009 | C2 | direct (N × H) |
| 4. C2×#16814656 | C2 | semidirect |
| 5. C2×#16814655 | C2 | semidirect |
| 6. C2×#16814651 | C2 | semidirect |
| 7. C2×C8×D229 | C2 | semidirect |
| 8. C2×SD16×C229 | C2 | semidirect |
| 10. #16814667 | C22 | semidirect |
| 12. #16814665 | C22 | semidirect |
| 20. #16814656 | C22 | semidirect |
| 21. #16814655 | C22 | semidirect |
| 22. #16814651 | C22 | semidirect |
| 24. C8×D229 | C22 | semidirect |
| 27. SD16×C229 | C22 | semidirect |
| 65. C2×C229 | #135 | semidirect |
| 69. C229 | C2×#135 | semidirect |
| 76. C2×SD16 | D229 | semidirect |
| 94. SD16 | C2×D229 | semidirect |
| 137. C2 | #20301009 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16814667 | 2 |
| C2×#16814665 | 2 |
| #20301009 | 2 |
| C2×#16814656 | 2 |
| C2×#16814655 | 2 |
| C2×#16814651 | 2 |
| C2×C8×D229 | 2 |
| C2×SD16×C229 | 2 |
| C2×#135 | 229 |