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. #11927094 | C2 | semidirect |
| 2. C2×#10597321 | C2 | semidirect |
| 3. #11926933 | C2 | semidirect |
| 4. #11926904 | C2 | semidirect |
| 5. #11926760 | C2 | semidirect |
| 6. #11926685 | C2 | semidirect |
| 7. #11926680 | C2 | semidirect |
| 8. C19×#432 | C2 | semidirect |
| 18. C2×#64516 | C22 | semidirect |
| 24. #10597320 | C22 | semidirect |
| 26. C4×D76 | C22 | semidirect |
| 27. #10597315 | C22 | semidirect |
| 28. C19×C4⋊C8 | C22 | semidirect |
| 30. C19×#97 | C22 | semidirect |
| 32. #10597273 | C22 | semidirect |
| 122. #432 | D19 | semidirect |
| 148. C4⋊C8 | C2×D19 | semidirect |
| 152. #97 | 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 |
|---|---|
| #11927094 | 2 |
| C2×#10597321 | 2 |
| #11926933 | 2 |
| #11926904 | 2 |
| #11926760 | 2 |
| #11926685 | 2 |
| #11926680 | 2 |
| C19×#432 | 2 |
| #3213 | 19 |