Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
576 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 3. #20298621 | C2 | direct (N × H) |
| 4. C2×#16813551 | C2 | semidirect |
| 15. #16813551 | C22 | semidirect |
| 56. C2×Dic113 | M16 | semidirect |
| 72. Dic113 | C2×M16 | semidirect |
| 74. C2×C113 | #423 | semidirect |
| 78. C113 | C2×#423 | semidirect |
| 152. C2 | #20298621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268631 | 2 |
| C22×C4×Dic113 | 2 |
| #20298621 | 2 |
| C2×#16813551 | 2 |
| C22×M16×C113 | 2 |
| C2×#423 | 113 |