Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×#11744762 | C2 | semidirect |
| 3. #20299687 | C2 | semidirect |
| 4. Q8⋊#11744762 | C2 | semidirect |
| 6. C8×#11744762 | C2 | semidirect |
| 39. #14268636 | C8 | semidirect |
| 40. #14268635 | C8 | semidirect |
| 41. #14268634 | C8 | semidirect |
| 43. SD16×C113 | C8 | semidirect |
| 55. #11744762 | SD16 | direct (N × H) |
| 56. Q8×C113 | C2×C8 | semidirect |
| 63. Dic226 | C2×C8 | semidirect |
| 65. C8×C113 | C2×C8 | semidirect |
| 66. #11744751 | C2×C8 | semidirect |
| 87. C113 | C8×SD16 | semidirect |
| 116. SD16 | #11744762 | direct (N × H) |
| 134. Q8 | C2×#11744762 | semidirect |
| 153. C8 | C2×#11744762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11744762 | 2 |
| D4×#11744762 | 2 |
| #20299687 | 2 |
| Q8⋊#11744762 | 2 |
| D4⋊#11744762 | 2 |
| C8×#11744762 | 2 |
| SD16×#90673 | 2 |
| C8×SD16 | 113 |