Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D113 | C2 | semidirect |
| 2. C2×#16813654 | C2 | semidirect |
| 4. #20298753 | C2 | semidirect |
| 5. #20298752 | C2 | semidirect |
| 6. #20298739 | C2 | semidirect |
| 7. #20298738 | C2 | semidirect |
| 8. #20298737 | C2 | semidirect |
| 9. #20298605 | C2 | semidirect |
| 10. #20298560 | C2 | semidirect |
| 11. #451×C113 | C2 | semidirect |
| 23. C2×#14268637 | C22 | semidirect |
| 24. C2×#14268636 | C22 | semidirect |
| 25. C2×#14268634 | C22 | semidirect |
| 35. #16813547 | C22 | semidirect |
| 36. #16813546 | C22 | semidirect |
| 37. #16813545 | C22 | semidirect |
| 41. C2×Q16×C113 | C22 | semidirect |
| 43. #103×C113 | C22 | semidirect |
| 58. Q8×D113 | D4 | semidirect |
| 141. C22×C113 | #137 | semidirect |
| 152. C2×D113 | #137 | semidirect |
| 170. C113 | #3004 | semidirect |
| 176. #451 | D113 | semidirect |
| 195. C2×Q16 | C2×D113 | semidirect |
| 211. #103 | C2×D113 | semidirect |
| 321. C22 | #16813654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D113 | 2 |
| C2×#16813654 | 2 |
| #20299111 | 2 |
| #20298753 | 2 |
| #20298752 | 2 |
| #20298739 | 2 |
| #20298738 | 2 |
| #20298737 | 2 |
| #20298605 | 2 |
| #20298560 | 2 |
| #451×C113 | 2 |
| #3004 | 113 |