Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 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. #20299633 | C2 | semidirect |
| 2. #20299632 | C2 | semidirect |
| 3. #20299462 | C2 | semidirect |
| 4. #20299446 | C2 | semidirect |
| 5. D4⋊#11744753 | C2 | semidirect |
| 6. C8×#11744753 | C2 | semidirect |
| 61. #11744753 | D8 | semidirect |
| 63. #11744751 | M16 | semidirect |
| 84. C113 | #1589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299633 | 2 |
| #20299632 | 2 |
| #20299462 | 2 |
| #20299446 | 2 |
| D4⋊#11744753 | 2 |
| C8×#11744753 | 2 |
| #20298678 | 2 |
| #1589 | 113 |