Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D113⋊#131 | C2 | semidirect |
| 2. #20299667 | C2 | semidirect |
| 3. #20299590 | C2 | semidirect |
| 4. #20299589 | C2 | semidirect |
| 5. #20299588 | C2 | semidirect |
| 6. C2×#16813684 | C2 | semidirect |
| 10. D113⋊M16 | C22 | semidirect |
| 11. C2×#14268655 | C22 | semidirect |
| 14. #16813701 | C22 | semidirect |
| 15. C2×C4⋊#90673 | C22 | semidirect |
| 16. #16813685 | C22 | semidirect |
| 17. #16813685 | C22 | semidirect |
| 18. #16813684 | C22 | semidirect |
| 19. #16813684 | C22 | semidirect |
| 20. #16813684 | C22 | semidirect |
| 22. #16813668 | C4 | semidirect |
| 23. #16813668 | C4 | semidirect |
| 25. #16813667 | C4 | semidirect |
| 31. H(5,𝔽2)×C113 | C4 | semidirect |
| 46. #14268648 | C2×C4 | semidirect |
| 51. #14268647 | C2×C4 | semidirect |
| 54. #14268646 | C2×C4 | semidirect |
| 59. C2×D452 | C2×C4 | semidirect |
| 68. D4×D113 | C2×C4 | semidirect |
| 75. #41×C113 | C2×C4 | semidirect |
| 77. C2×D4×C113 | C2×C4 | semidirect |
| 147. C113 | #2897 | semidirect |
| 160. H(5,𝔽2) | #90673 | semidirect |
| 193. #41 | C2×#90673 | semidirect |
| 210. C2×D4 | C2×#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D113⋊#131 | 2 |
| #20299667 | 2 |
| #20299590 | 2 |
| #20299589 | 2 |
| #20299588 | 2 |
| C2×#16813684 | 2 |
| H(5,𝔽2)×D113 | 2 |
| #2897 | 113 |