Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597378 | C2 | semidirect |
| 2. C2×#10597395 | C2 | semidirect |
| 3. C2×#10597396 | C2 | semidirect |
| 4. C22×#64525 | C2 | semidirect |
| 5. #11927113 | C2 | semidirect |
| 6. #11926934 | C2 | semidirect |
| 7. #11926931 | C2 | semidirect |
| 8. #11926926 | C2 | semidirect |
| 9. #11926920 | C2 | semidirect |
| 10. #11926500 | C2 | semidirect |
| 11. C19×#535 | C2 | semidirect |
| 16. C19×#127 | C22 | semidirect |
| 17. C19×#124 | C22 | semidirect |
| 23. C2×#64528 | C22 | semidirect |
| 24. C2×#64527 | C22 | semidirect |
| 25. C2×#64527 | C22 | semidirect |
| 26. C2×#64526 | C22 | semidirect |
| 27. C2×#64526 | C22 | semidirect |
| 32. C2×#64525 | C22 | semidirect |
| 33. C2×#64525 | C22 | semidirect |
| 34. C2×#64525 | C22 | semidirect |
| 39. #10597321 | C22 | semidirect |
| 40. #10597320 | C22 | semidirect |
| 41. #10597260 | C22 | semidirect |
| 42. C4×C19⋊C8 | C22 | semidirect |
| 83. #64520 | D4 | semidirect |
| 84. C2×C19⋊C8 | D4 | semidirect |
| 152. #535 | D19 | semidirect |
| 186. #127 | C2×D19 | semidirect |
| 188. #124 | C2×D19 | semidirect |
| 196. C19 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597378 | 2 |
| C2×#10597395 | 2 |
| C2×#10597396 | 2 |
| C22×#64525 | 2 |
| #11927113 | 2 |
| #11926934 | 2 |
| #11926931 | 2 |
| #11926926 | 2 |
| #11926920 | 2 |
| #11926500 | 2 |
| C19×#535 | 2 |
| #3155 | 19 |