Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597362 | C2 | semidirect |
| 2. #11927216 | C2 | semidirect |
| 3. #11927214 | C2 | semidirect |
| 4. #11926920 | C2 | semidirect |
| 5. #11926779 | C2 | semidirect |
| 6. #11926745 | C2 | semidirect |
| 7. #11926690 | C2 | semidirect |
| 8. #11926688 | C2 | semidirect |
| 9. C4×#64528 | C2 | semidirect |
| 10. #11926609 | C2 | semidirect |
| 11. C19×#460 | C2 | semidirect |
| 69. #64528 | D4 | semidirect |
| 131. C4×C19 | #135 | semidirect |
| 143. #460 | D19 | semidirect |
| 184. C19 | #3287 | semidirect |
| 276. C4 | #10597362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597362 | 2 |
| #11927216 | 2 |
| #11927214 | 2 |
| #11926920 | 2 |
| #11926779 | 2 |
| #11926745 | 2 |
| #11926690 | 2 |
| #11926688 | 2 |
| C4×#64528 | 2 |
| #11926609 | 2 |
| C19×#460 | 2 |
| #3287 | 19 |