Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #20299321 | C2 | semidirect |
| 2. #20299308 | C2 | semidirect |
| 3. #20298953 | C2 | semidirect |
| 4. #20298949 | C2 | semidirect |
| 5. #20298906 | C2 | semidirect |
| 6. #20298889 | C2 | semidirect |
| 8. #20298804 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 11. C8×Q8×C113 | C2 | semidirect |
| 121. C113 | #3360 | semidirect |
| 130. C8×Q8 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299321 | 2 |
| #20299308 | 2 |
| #20298953 | 2 |
| #20298949 | 2 |
| #20298906 | 2 |
| #20298889 | 2 |
| #20298814 | 2 |
| #20298804 | 2 |
| C4×#14268636 | 2 |
| C4×D904 | 2 |
| C8×Q8×C113 | 2 |
| #3360 | 113 |