Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 698 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. 2−1+4×D19 | C2 | semidirect |
| 2. #11927343 | C2 | semidirect |
| 3. #11927119 | C2 | semidirect |
| 4. #11926726 | C2 | semidirect |
| 5. #11926725 | C2 | semidirect |
| 6. #11926719 | C2 | semidirect |
| 7. #11926718 | C2 | semidirect |
| 8. #11926717 | C2 | semidirect |
| 9. #11926559 | C2 | semidirect |
| 10. #101×D19 | C2 | semidirect |
| 11. C19×#456 | C2 | semidirect |
| 24. C19×#137 | C22 | semidirect |
| 25. C19×C4⋊Q8 | C22 | semidirect |
| 26. #10597395 | C22 | semidirect |
| 27. #10597393 | C22 | semidirect |
| 28. #10597390 | C22 | semidirect |
| 29. #10597388 | C22 | semidirect |
| 34. #10597354 | C22 | semidirect |
| 38. #10597321 | C22 | semidirect |
| 40. C19×#104 | C22 | semidirect |
| 41. C19×#101 | C22 | semidirect |
| 42. #10597294 | C22 | semidirect |
| 43. #10597293 | C22 | semidirect |
| 44. #10597282 | C22 | semidirect |
| 45. #10597281 | C22 | semidirect |
| 46. #10597262 | C22 | semidirect |
| 184. #456 | D19 | semidirect |
| 211. #137 | C2×D19 | semidirect |
| 219. C4⋊Q8 | C2×D19 | semidirect |
| 228. #104 | C2×D19 | semidirect |
| 231. #101 | C2×D19 | semidirect |
| 232. C19 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 2−1+4×D19 | 2 |
| #11927343 | 2 |
| #11927119 | 2 |
| #11926726 | 2 |
| #11926725 | 2 |
| #11926719 | 2 |
| #11926718 | 2 |
| #11926717 | 2 |
| #11926559 | 2 |
| #101×D19 | 2 |
| C19×#456 | 2 |
| #3020 | 19 |