Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10597321 | C2 | semidirect |
| 2. #11926931 | C2 | semidirect |
| 3. #11926906 | C2 | semidirect |
| 4. #11926759 | C2 | semidirect |
| 5. #11926682 | C2 | semidirect |
| 6. #11926677 | C2 | semidirect |
| 7. #11926601 | C2 | semidirect |
| 8. C19×#532 | C2 | semidirect |
| 12. C19×C4⋊Q8 | C22 | semidirect |
| 13. C19×#127 | C22 | semidirect |
| 18. C4×D4×C19 | C22 | semidirect |
| 20. C2×#64526 | C22 | semidirect |
| 29. #10597267 | C22 | semidirect |
| 31. C4⋊(C19⋊C8) | C22 | semidirect |
| 32. #10597260 | C22 | semidirect |
| 115. #532 | D19 | semidirect |
| 134. C4⋊Q8 | C2×D19 | semidirect |
| 135. #127 | C2×D19 | semidirect |
| 144. C4×D4 | C2×D19 | semidirect |
| 153. C19 | #3213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597321 | 2 |
| #11926931 | 2 |
| #11926906 | 2 |
| #11926759 | 2 |
| #11926682 | 2 |
| #11926677 | 2 |
| #11926601 | 2 |
| C19×#532 | 2 |
| #3213 | 19 |