Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
402 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20299155 | C2 | semidirect |
| 3. #20299003 | C2 | semidirect |
| 4. #20298971 | C2 | semidirect |
| 5. #20298949 | C2 | semidirect |
| 6. #20298945 | C2 | semidirect |
| 7. #20298844 | C2 | semidirect |
| 8. #20298700 | C2 | semidirect |
| 9. C4×M16×C113 | C2 | semidirect |
| 90. C8×C113 | #41 | semidirect |
| 113. C113 | #3182 | semidirect |
| 122. C4×M16 | D113 | semidirect |
| 203. C8 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299155 | 2 |
| #20299148 | 2 |
| #20299003 | 2 |
| #20298971 | 2 |
| #20298949 | 2 |
| #20298945 | 2 |
| #20298844 | 2 |
| #20298700 | 2 |
| C4×M16×C113 | 2 |
| #3182 | 113 |