Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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. C2×#16813644 | C2 | semidirect |
| 2. #20299269 | C2 | semidirect |
| 3. #20299253 | C2 | semidirect |
| 4. #20298971 | C2 | semidirect |
| 5. #20298827 | C2 | semidirect |
| 6. #20298809 | C2 | semidirect |
| 7. #20298794 | C2 | semidirect |
| 8. #20298762 | C2 | semidirect |
| 9. #20298745 | C2 | semidirect |
| 10. C4×#14268636 | C2 | semidirect |
| 11. C8×D4×C113 | C2 | semidirect |
| 61. #14268636 | D4 | semidirect |
| 127. C4×C113 | #135 | semidirect |
| 141. C113 | #3284 | semidirect |
| 152. C8×D4 | D113 | semidirect |
| 272. C4 | #16813644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813644 | 2 |
| #20299269 | 2 |
| #20299253 | 2 |
| #20298971 | 2 |
| #20298827 | 2 |
| #20298809 | 2 |
| #20298794 | 2 |
| #20298762 | 2 |
| #20298745 | 2 |
| C4×#14268636 | 2 |
| C8×D4×C113 | 2 |
| #3284 | 113 |