Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #20298996 | C2 | semidirect |
| 3. #20298883 | C2 | semidirect |
| 5. #20298343 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 52. Q8×C113 | SD16 | semidirect |
| 93. C113 | #1651 | semidirect |
| 99. Q8⋊C8 | D113 | semidirect |
| 150. Q8 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D452 | 2 |
| #20298996 | 2 |
| #20298883 | 2 |
| #20298804 | 2 |
| #20298343 | 2 |
| #20298327 | 2 |
| Q8⋊C8×C113 | 2 |
| #1651 | 113 |