Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#10597274 | C2 | semidirect |
| 3. C2×#10597273 | C2 | semidirect |
| 5. #11926450 | C2 | semidirect |
| 7. C2×C4×C8×C19 | C2 | semidirect |
| 18. C2×#64516 | C4 | semidirect |
| 64. C2×C4×C19 | SD16 | semidirect |
| 87. C8×C19 | C22⋊C4 | semidirect |
| 111. C2×C4×C8 | D19 | semidirect |
| 136. C19 | #1968 | semidirect |
| 192. C2×C4 | #64516 | semidirect |
| 200. C8 | (C2×D19)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64516 | 2 |
| C2×#10597274 | 2 |
| C2×#10597273 | 2 |
| C2×#10597278 | 2 |
| #11926450 | 2 |
| #11926446 | 2 |
| C2×C4×C8×C19 | 2 |
| #1968 | 19 |