Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20298330 | C2 | semidirect |
| 5. Q8⋊#11744751 | C2 | semidirect |
| 6. #20298328 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 59. Q8×C113 | M16 | semidirect |
| 79. Dic226 | M16 | semidirect |
| 105. C113 | #1491 | semidirect |
| 112. Q8⋊C8 | D113 | semidirect |
| 167. Q8 | #14268630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D113 | 2 |
| #20298654 | 2 |
| C4×#14268630 | 2 |
| #20298330 | 2 |
| Q8⋊#11744751 | 2 |
| #20298328 | 2 |
| Q8⋊C8×C113 | 2 |
| #1491 | 113 |