Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14268634 | C2 | semidirect |
| 3. #20299076 | C2 | semidirect |
| 4. #20298822 | C2 | semidirect |
| 5. #20298796 | C2 | semidirect |
| 6. #20298626 | C2 | semidirect |
| 7. #20298604 | C2 | semidirect |
| 8. #20298594 | C2 | semidirect |
| 9. C2×#137×C113 | C2 | semidirect |
| 19. Q8×Dic113 | C22 | semidirect |
| 23. #16813551 | C22 | semidirect |
| 24. #16813546 | C22 | semidirect |
| 26. #16813543 | C22 | semidirect |
| 30. C2×Q16×C113 | C22 | semidirect |
| 31. C2×SD16×C113 | C22 | semidirect |
| 55. C2×Q8×C113 | D4 | semidirect |
| 117. C113 | #3043 | semidirect |
| 118. C2×#137 | D113 | semidirect |
| 131. C2×Q16 | C2×D113 | semidirect |
| 134. C2×SD16 | C2×D113 | semidirect |
| 155. C2×Q8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268634 | 2 |
| #20299162 | 2 |
| #20299076 | 2 |
| #20298822 | 2 |
| #20298796 | 2 |
| #20298626 | 2 |
| #20298604 | 2 |
| #20298594 | 2 |
| C2×#137×C113 | 2 |
| #3043 | 113 |