Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 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×D452 | C2 | semidirect |
| 2. #20298945 | C2 | semidirect |
| 3. #20298798 | C2 | semidirect |
| 5. #20298343 | C2 | semidirect |
| 6. #20298327 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 54. Q8×C113 | D8 | semidirect |
| 68. D452 | SD16 | semidirect |
| 100. C113 | #1627 | semidirect |
| 106. Q8⋊C8 | D113 | semidirect |
| 157. Q8 | D904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D452 | 2 |
| #20298945 | 2 |
| #20298798 | 2 |
| #20298794 | 2 |
| #20298343 | 2 |
| #20298327 | 2 |
| Q8⋊C8×C113 | 2 |
| #1627 | 113 |