Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic38 | C2 | semidirect |
| 2. C22×#64516 | C2 | semidirect |
| 4. #11926685 | C2 | direct (N × H) |
| 5. C2×#10597273 | C2 | semidirect |
| 6. C2×C19×C22⋊C8 | C2 | semidirect |
| 15. C22×Dic38 | C22 | semidirect |
| 22. C2×#64516 | C22 | semidirect |
| 23. C19×C22⋊C8 | C22 | semidirect |
| 24. #10597273 | C22 | semidirect |
| 47. C2×Dic38 | D4 | semidirect |
| 57. C23×C19 | SD16 | semidirect |
| 82. Dic38 | C2×D4 | semidirect |
| 90. C22×C19 | C2×SD16 | semidirect |
| 107. C2×C22⋊C8 | D19 | semidirect |
| 109. C2×C19 | #448 | semidirect |
| 131. C22⋊C8 | C2×D19 | semidirect |
| 132. C19 | C2×#448 | semidirect |
| 169. C23 | #64516 | semidirect |
| 201. C22 | C2×#64516 | semidirect |
| 211. C2 | #11926685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic38 | 2 |
| C22×#64516 | 2 |
| C2×#10597376 | 2 |
| #11926685 | 2 |
| C2×#10597273 | 2 |
| C2×C19×C22⋊C8 | 2 |
| C2×#448 | 19 |