Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #20298935 | C2 | semidirect |
| 3. #20298890 | C2 | semidirect |
| 4. #20298840 | C2 | semidirect |
| 5. C4×Dic452 | C2 | semidirect |
| 7. #107×D113 | C2 | semidirect |
| 8. #500×C113 | C2 | semidirect |
| 58. D452 | Q16 | semidirect |
| 84. C113 | #3338 | semidirect |
| 86. #500 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299309 | 2 |
| #20298935 | 2 |
| #20298890 | 2 |
| #20298840 | 2 |
| C4×Dic452 | 2 |
| C8×D452 | 2 |
| #107×D113 | 2 |
| #500×C113 | 2 |
| #3338 | 113 |