Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#10597354 | C2 | semidirect |
| 2. #11927215 | C2 | semidirect |
| 3. D4×D76 | C2 | semidirect |
| 4. #11926921 | C2 | semidirect |
| 5. #11926797 | C2 | semidirect |
| 6. #11926745 | C2 | semidirect |
| 7. #11926740 | C2 | semidirect |
| 8. #11926691 | C2 | semidirect |
| 9. #11926680 | C2 | semidirect |
| 10. C4×#64516 | C2 | semidirect |
| 11. C19×#436 | C2 | semidirect |
| 13. C2×#64541 | C22 | semidirect |
| 15. C2×M16×C19 | C22 | semidirect |
| 19. #10597376 | C22 | semidirect |
| 22. C2×D152 | C22 | semidirect |
| 23. C2×D152 | C22 | semidirect |
| 25. C2×#64516 | C22 | semidirect |
| 31. #10597320 | C22 | semidirect |
| 33. C4×Dic38 | C22 | semidirect |
| 34. C19×C4⋊C8 | C22 | semidirect |
| 35. C19×C22⋊C8 | C22 | semidirect |
| 36. C4×C8×C19 | C22 | semidirect |
| 38. #10597278 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. #10597274 | C22 | semidirect |
| 41. #10597273 | C22 | semidirect |
| 82. #64516 | D4 | semidirect |
| 117. Dic38 | C2×D4 | semidirect |
| 120. C8×C19 | C2×D4 | semidirect |
| 138. C4×C19 | AGL(1,ℤ/8) | semidirect |
| 154. #436 | D19 | semidirect |
| 171. C2×M16 | C2×D19 | semidirect |
| 185. C4⋊C8 | C2×D19 | semidirect |
| 190. C22⋊C8 | C2×D19 | semidirect |
| 191. C4×C8 | C2×D19 | semidirect |
| 192. C19 | #3274 | semidirect |
| 271. C8 | D4×D19 | semidirect |
| 291. C4 | #10597354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597354 | 2 |
| #11927215 | 2 |
| D4×D76 | 2 |
| #11926921 | 2 |
| #11926797 | 2 |
| #11926745 | 2 |
| #11926740 | 2 |
| #11926691 | 2 |
| #11926680 | 2 |
| C4×#64516 | 2 |
| C19×#436 | 2 |
| #3274 | 19 |