Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11926949 | C2 | semidirect |
| 3. #11926948 | C2 | semidirect |
| 4. #11926947 | C2 | semidirect |
| 7. C19×#500 | C2 | semidirect |
| 44. C8×D19 | Q8 | semidirect |
| 61. C8×C19 | C2×Q8 | semidirect |
| 62. C19⋊C8 | C2×Q8 | semidirect |
| 80. #500 | D19 | direct (N × H) |
| 86. D19 | #500 | direct (N × H) |
| 103. C19 | C2×#500 | semidirect |
| 142. C8 | Q8×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D19 | 2 |
| #11926949 | 2 |
| #11926948 | 2 |
| #11926947 | 2 |
| #107×D19 | 2 |
| C4×C8×D19 | 2 |
| C19×#500 | 2 |
| C2×#500 | 19 |