Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
616 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 234 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×#14268655 | C2 | semidirect |
| 2. #20299626 | C2 | direct (N × H) |
| 3. C2×C4⋊#11744753 | C2 | semidirect |
| 4. C2×#16813679 | C2 | semidirect |
| 5. C2×C4×#11744753 | C2 | semidirect |
| 8. C2×#14268655 | C22 | semidirect |
| 12. C4⋊#11744753 | C22 | semidirect |
| 13. #16813679 | C22 | semidirect |
| 14. C4×#11744753 | C22 | semidirect |
| 25. C2×#11744753 | D4 | semidirect |
| 30. C2×D452 | C8 | semidirect |
| 47. C22×D113 | C2×C8 | semidirect |
| 50. C2×C4×C113 | C2×C8 | semidirect |
| 59. D452 | C2×C8 | semidirect |
| 65. #11744753 | C2×D4 | semidirect |
| 73. C2×D113 | C22×C8 | semidirect |
| 75. C4×C113 | C22×C8 | semidirect |
| 80. C2×C113 | C8×D4 | semidirect |
| 86. C113 | C2×C8×D4 | semidirect |
| 146. C2×C4 | #14268655 | semidirect |
| 165. C4 | C2×#14268655 | semidirect |
| 167. C2 | #20299626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268655 | 2 |
| #20299626 | 2 |
| C2×C4⋊#11744753 | 2 |
| C2×#16813679 | 2 |
| C2×C4×#11744753 | 2 |
| C2×#16813584 | 2 |
| C2×C8×D4 | 113 |