Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#16813654 | C2 | semidirect |
| 3. Q8×D452 | C2 | semidirect |
| 4. #20298971 | C2 | semidirect |
| 5. #20298845 | C2 | semidirect |
| 6. #20298808 | C2 | semidirect |
| 7. #20298798 | C2 | semidirect |
| 8. #20298763 | C2 | semidirect |
| 9. #20298738 | C2 | semidirect |
| 10. #20298677 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 72. Q16×C113 | D4 | semidirect |
| 126. C4×C113 | #137 | semidirect |
| 137. C113 | #3278 | semidirect |
| 147. C4×Q16 | D113 | semidirect |
| 197. Q16 | D452 | semidirect |
| 265. C4 | #16813654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813654 | 2 |
| #20299270 | 2 |
| Q8×D452 | 2 |
| #20298971 | 2 |
| #20298845 | 2 |
| #20298808 | 2 |
| #20298798 | 2 |
| #20298763 | 2 |
| #20298738 | 2 |
| #20298677 | 2 |
| C4×Q16×C113 | 2 |
| #3278 | 113 |