Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #20298990 | C2 | semidirect |
| 3. #20298960 | C2 | semidirect |
| 4. #20298820 | C2 | semidirect |
| 5. #20298753 | C2 | semidirect |
| 7. #20298655 | C2 | semidirect |
| 8. #533×C113 | C2 | semidirect |
| 11. C2×#14268637 | C22 | semidirect |
| 19. C4⋊#11744751 | C22 | semidirect |
| 20. #16813545 | C22 | semidirect |
| 23. #16813533 | C22 | semidirect |
| 24. C4⋊Q8×C113 | C22 | semidirect |
| 25. C4⋊Q8×C113 | C22 | semidirect |
| 30. C4×Q8×C113 | C22 | semidirect |
| 113. C113 | #3215 | semidirect |
| 114. #533 | D113 | semidirect |
| 126. C4⋊Q8 | C2×D113 | semidirect |
| 127. C4⋊Q8 | C2×D113 | semidirect |
| 136. C4×Q8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813610 | 2 |
| #20298990 | 2 |
| #20298960 | 2 |
| #20298820 | 2 |
| #20298753 | 2 |
| #20298748 | 2 |
| #20298655 | 2 |
| #533×C113 | 2 |
| #3215 | 113 |