Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#10597260 | C2 | semidirect |
| 4. #11926306 | C2 | semidirect |
| 5. C4×C4⋊C4×C19 | C2 | semidirect |
| 15. C4×D76 | C4 | semidirect |
| 17. #10597266 | C4 | semidirect |
| 32. C4⋊C4×C19 | C2×C4 | semidirect |
| 41. C2×C19⋊C8 | C2×C4 | semidirect |
| 64. D76 | C42 | semidirect |
| 88. C4×C4⋊C4 | D19 | semidirect |
| 109. C19 | #1762 | semidirect |
| 128. C4⋊C4 | C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D76 | 2 |
| C2×#10597266 | 2 |
| C2×#10597260 | 2 |
| #11926306 | 2 |
| C4×C4⋊C4×C19 | 2 |
| #1762 | 19 |