Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D76 | C2 | semidirect |
| 2. C2×#10597354 | C2 | semidirect |
| 3. #11927055 | C2 | semidirect |
| 4. #11926697 | C2 | semidirect |
| 5. #11926680 | C2 | semidirect |
| 6. #11926550 | C2 | semidirect |
| 7. C19×#407 | C2 | semidirect |
| 10. C2×#64541 | C22 | semidirect |
| 16. C2×M16×C19 | C22 | semidirect |
| 18. #10597376 | C22 | semidirect |
| 21. #10597372 | C22 | semidirect |
| 22. #10597370 | C22 | semidirect |
| 24. C2×D152 | C22 | semidirect |
| 25. C2×#64516 | C22 | semidirect |
| 26. C19×C22⋊C8 | C22 | semidirect |
| 27. #10597278 | C22 | semidirect |
| 47. C2×D76 | D4 | semidirect |
| 49. C2×D76 | C23 | semidirect |
| 51. C2×Dic38 | C23 | semidirect |
| 53. C2×C8×C19 | C23 | semidirect |
| 57. C4⋊Dic19 | C23 | semidirect |
| 99. C22×C19 | AGL(1,ℤ/8) | semidirect |
| 118. #407 | D19 | semidirect |
| 136. C2×M16 | C2×D19 | semidirect |
| 144. C22⋊C8 | C2×D19 | semidirect |
| 145. C19 | #3003 | semidirect |
| 173. C2×C8 | C22×D19 | semidirect |
| 222. C22 | #10597354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D76 | 2 |
| C2×#10597354 | 2 |
| #11927055 | 2 |
| #11926697 | 2 |
| #11926680 | 2 |
| #11926550 | 2 |
| C19×#407 | 2 |
| #3003 | 19 |