Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
792 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#14268634 | C2 | semidirect |
| 3. #20298737 | C2 | direct (N × H) |
| 4. C2×#16813546 | C2 | semidirect |
| 5. C2×C22⋊#11744751 | C2 | semidirect |
| 6. C23×Q8×C113 | C2 | semidirect |
| 10. C2×#14268634 | C22 | semidirect |
| 16. #16813546 | C22 | semidirect |
| 17. C22⋊#11744751 | C22 | semidirect |
| 22. C22×Q8×C113 | C22 | semidirect |
| 45. C2×Q8×C113 | D4 | semidirect |
| 57. C23×C113 | SD16 | semidirect |
| 67. Q8×C113 | C2×D4 | semidirect |
| 89. C22×C113 | C2×SD16 | semidirect |
| 102. C2×C113 | #448 | semidirect |
| 108. C113 | C2×#448 | semidirect |
| 109. C23×Q8 | D113 | semidirect |
| 119. C22×Q8 | C2×D113 | semidirect |
| 141. C2×Q8 | C22⋊D113 | semidirect |
| 169. C23 | #14268634 | semidirect |
| 175. Q8 | C2×C22⋊D113 | semidirect |
| 201. C22 | C2×#14268634 | semidirect |
| 211. C2 | #20298737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268634 | 2 |
| C2×#16813596 | 2 |
| #20298737 | 2 |
| C2×#16813546 | 2 |
| C2×C22⋊#11744751 | 2 |
| C23×Q8×C113 | 2 |
| C2×#448 | 113 |