Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #20299645 | C2 | semidirect |
| 2. #20299639 | C2 | semidirect |
| 3. #20299523 | C2 | semidirect |
| 4. #20299516 | C2 | semidirect |
| 5. #20299514 | C2 | semidirect |
| 6. #20299489 | C2 | semidirect |
| 18. #16813567 | C4 | semidirect |
| 19. #16813566 | C4 | semidirect |
| 20. #16813563 | C4 | semidirect |
| 22. D16×C113 | C4 | semidirect |
| 34. Dic452 | C2×C4 | semidirect |
| 39. #14268622 | C2×C4 | semidirect |
| 41. D8×C113 | C2×C4 | semidirect |
| 42. C16×C113 | C2×C4 | semidirect |
| 76. C113 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #90673 | semidirect |
| 107. D8 | C2×#90673 | semidirect |
| 118. C16 | C2×#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299645 | 2 |
| #20299639 | 2 |
| #20299523 | 2 |
| #20299516 | 2 |
| #20299514 | 2 |
| #20299489 | 2 |
| #20299032 | 2 |
| AGL(1,ℤ/16) | 113 |