Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×C16×D113 | C2 | semidirect |
| 3. #20298377 | C2 | semidirect |
| 4. C4×#14268622 | C2 | semidirect |
| 5. C4⋊C16×C113 | C2 | semidirect |
| 23. #14268622 | D4 | semidirect |
| 33. D452 | C16 | semidirect |
| 43. C2×D113 | C2×C16 | semidirect |
| 45. C4×C113 | C2×C16 | semidirect |
| 54. C113 | D4×C16 | semidirect |
| 57. C4⋊C16 | D113 | semidirect |
| 100. C4 | C16×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D113 | 2 |
| C8×D452 | 2 |
| #20298377 | 2 |
| C4×#14268622 | 2 |
| C4⋊C16×C113 | 2 |
| D4×C16 | 113 |