Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×D76 | C2 | semidirect |
| 2. #11926855 | C2 | semidirect |
| 3. #11926821 | C2 | semidirect |
| 4. #11926736 | C2 | semidirect |
| 5. #11926677 | C2 | semidirect |
| 6. C4×#64525 | C2 | semidirect |
| 7. #11926597 | C2 | semidirect |
| 8. C19×#532 | C2 | semidirect |
| 12. C19×C4⋊Q8 | C22 | semidirect |
| 13. C19×#127 | C22 | semidirect |
| 18. C4×D4×C19 | C22 | semidirect |
| 27. #10597289 | C22 | semidirect |
| 30. #10597264 | C22 | semidirect |
| 31. C4⋊(C19⋊C8) | C22 | semidirect |
| 32. C4×C19⋊C8 | C22 | semidirect |
| 80. C2×C4×C19 | D8 | semidirect |
| 91. D76 | #41 | semidirect |
| 115. #532 | D19 | semidirect |
| 133. C4⋊Q8 | C2×D19 | semidirect |
| 134. #127 | C2×D19 | semidirect |
| 143. C4×D4 | C2×D19 | semidirect |
| 153. C19 | #3100 | semidirect |
| 208. C2×C4 | #64525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D76 | 2 |
| #11926855 | 2 |
| #11926821 | 2 |
| #11926736 | 2 |
| #11926677 | 2 |
| C4×#64525 | 2 |
| #11926597 | 2 |
| C19×#532 | 2 |
| #3100 | 19 |