Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597355 | C2 | semidirect |
| 3. C2×#10597315 | C2 | semidirect |
| 4. #11926938 | C2 | semidirect |
| 5. #11926924 | C2 | semidirect |
| 6. #11926917 | C2 | semidirect |
| 7. C4×M16×C19 | C2 | semidirect |
| 38. M16×C19 | D4 | semidirect |
| 76. C4×C19 | #137 | semidirect |
| 86. C4×M16 | D19 | semidirect |
| 109. C19 | #3152 | semidirect |
| 124. M16 | D76 | semidirect |
| 161. C4 | #10597355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597355 | 2 |
| #11927094 | 2 |
| C2×#10597315 | 2 |
| #11926938 | 2 |
| #11926924 | 2 |
| #11926917 | 2 |
| C4×M16×C19 | 2 |
| #3152 | 19 |