Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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. D229⋊M16 | C2 | semidirect |
| 2. #20301067 | C2 | semidirect |
| 3. #20301050 | C2 | semidirect |
| 7. D229⋊C8 | C22 | semidirect |
| 8. C4⋊#11745021 | C22 | semidirect |
| 12. C2×D916 | C4 | semidirect |
| 16. D4×D229 | C4 | semidirect |
| 19. C2×D4×C229 | C4 | semidirect |
| 61. C229 | #418 | semidirect |
| 74. C2×D4 | #11745021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D229⋊M16 | 2 |
| #20301067 | 2 |
| #20301050 | 2 |
| C2×D4×D229 | 2 |
| #418 | 229 |