Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20299220 | C2 | semidirect |
| 2. #20299002 | C2 | semidirect |
| 3. #20298983 | C2 | semidirect |
| 4. #20298959 | C2 | semidirect |
| 5. #20298847 | C2 | semidirect |
| 6. #20298836 | C2 | semidirect |
| 8. #20298696 | C2 | semidirect |
| 9. C4×D904 | C2 | semidirect |
| 10. #20298552 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 118. C113 | #3175 | semidirect |
| 127. C4×Q16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299220 | 2 |
| #20299002 | 2 |
| #20298983 | 2 |
| #20298959 | 2 |
| #20298847 | 2 |
| #20298836 | 2 |
| #20298835 | 2 |
| #20298696 | 2 |
| C4×D904 | 2 |
| #20298552 | 2 |
| C4×Q16×C113 | 2 |
| #3175 | 113 |