Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20298949 | C2 | semidirect |
| 4. #20298808 | C2 | semidirect |
| 5. #20298346 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 60. D452 | Q16 | semidirect |
| 89. C113 | #1644 | semidirect |
| 95. Q8⋊C8 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299308 | 2 |
| #20298949 | 2 |
| #20298879 | 2 |
| #20298808 | 2 |
| #20298346 | 2 |
| #20298327 | 2 |
| Q8⋊C8×C113 | 2 |
| #1644 | 113 |