Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 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×#10597350 | C2 | semidirect |
| 2. #11927094 | C2 | semidirect |
| 3. #11926928 | C2 | semidirect |
| 4. #11926924 | C2 | semidirect |
| 5. #11926921 | C2 | semidirect |
| 6. #11926917 | C2 | semidirect |
| 7. C2×C4×C8×C19 | C2 | semidirect |
| 31. C2×C8×C19 | D4 | semidirect |
| 66. C4×C19 | #135 | semidirect |
| 75. C2×C4×C8 | D19 | semidirect |
| 95. C19 | #3147 | semidirect |
| 107. C2×C8 | D76 | semidirect |
| 139. C4 | #10597350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597350 | 2 |
| #11927094 | 2 |
| #11926928 | 2 |
| #11926924 | 2 |
| #11926921 | 2 |
| #11926917 | 2 |
| C2×C4×C8×C19 | 2 |
| #3147 | 19 |