Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299333 | C2 | semidirect |
| 2. #20299308 | C2 | semidirect |
| 3. #20298953 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298899 | C2 | semidirect |
| 6. #20298894 | C2 | semidirect |
| 7. #20298814 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. C4×D904 | C2 | semidirect |
| 11. C8×Q8×C113 | C2 | semidirect |
| 123. C113 | #3361 | semidirect |
| 132. C8×Q8 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299333 | 2 |
| #20299308 | 2 |
| #20298953 | 2 |
| #20298945 | 2 |
| #20298899 | 2 |
| #20298894 | 2 |
| #20298814 | 2 |
| #20298794 | 2 |
| C4×#14268636 | 2 |
| C4×D904 | 2 |
| C8×Q8×C113 | 2 |
| #3361 | 113 |