Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
992 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#64520 | C2 | semidirect |
| 3. C2×#10597280 | C2 | direct (N × H) |
| 4. C22×M16×C19 | C2 | semidirect |
| 14. C2×M16×C19 | C22 | semidirect |
| 17. C2×#64520 | C22 | semidirect |
| 19. #10597280 | C22 | direct (N × H) |
| 41. M16×C19 | C23 | semidirect |
| 44. #64520 | C23 | semidirect |
| 74. C22×C19 | #100 | semidirect |
| 88. C22×M16 | D19 | semidirect |
| 92. C2×C19 | C2×#100 | semidirect |
| 106. C2×M16 | C2×D19 | semidirect |
| 110. C19 | C22×#100 | semidirect |
| 134. M16 | C22×D19 | semidirect |
| 168. C22 | #10597280 | direct (N × H) |
| 179. C2 | C2×#10597280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D76 | 2 |
| C22×#64520 | 2 |
| C2×#10597280 | 2 |
| C22×M16×C19 | 2 |
| C22×#100 | 19 |