Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#16813691 | C2 | semidirect |
| 2. C2×#16813690 | C2 | semidirect |
| 4. #20299472 | C2 | semidirect |
| 13. C2×#14268631 | C4 | semidirect |
| 14. C2×#14268630 | C4 | semidirect |
| 15. C2×#14268630 | C4 | semidirect |
| 20. C2×M16×C113 | C4 | semidirect |
| 83. C8×C113 | C22⋊C4 | semidirect |
| 85. #11744751 | C22⋊C4 | semidirect |
| 114. C113 | #1809 | semidirect |
| 126. C2×M16 | #90673 | semidirect |
| 199. C8 | C22⋊#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813691 | 2 |
| C2×#16813690 | 2 |
| #20299540 | 2 |
| #20299472 | 2 |
| C2×M16×D113 | 2 |
| #1809 | 113 |