Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20298798 | C2 | semidirect |
| 3. #20298351 | C2 | semidirect |
| 4. #20298341 | C2 | semidirect |
| 5. C8×Q8×C113 | C2 | semidirect |
| 34. Q8×C113 | D8 | semidirect |
| 47. C8×C113 | SD16 | semidirect |
| 65. C113 | #1668 | semidirect |
| 68. C8×Q8 | D113 | semidirect |
| 99. Q8 | D904 | semidirect |
| 113. C8 | #14268634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20298975 | 2 |
| #20298798 | 2 |
| #20298351 | 2 |
| #20298341 | 2 |
| C8×Q8×C113 | 2 |
| #1668 | 113 |