Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20298970 | C2 | semidirect |
| 2. #20298878 | C2 | semidirect |
| 3. D4×#11744751 | C2 | semidirect |
| 4. #20298348 | C2 | semidirect |
| 5. #20298343 | C2 | semidirect |
| 6. #20298342 | C2 | semidirect |
| 51. D4×C113 | SD16 | semidirect |
| 65. #11744751 | D8 | semidirect |
| 86. C113 | #1665 | semidirect |
| 139. D4 | #14268635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20298970 | 2 |
| #20298878 | 2 |
| D4×#11744751 | 2 |
| #20298348 | 2 |
| #20298343 | 2 |
| #20298342 | 2 |
| #459×C113 | 2 |
| #1665 | 113 |