Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#10597347 | C2 | semidirect |
| 3. #11926623 | C2 | semidirect |
| 4. C8×D76 | C2 | semidirect |
| 5. #11926568 | C2 | semidirect |
| 6. #11926510 | C2 | semidirect |
| 7. C2×C4×C8×C19 | C2 | semidirect |
| 35. C2×C8×C19 | D4 | semidirect |
| 76. C4×C19 | #131 | semidirect |
| 86. C2×C4×C8 | D19 | semidirect |
| 108. C19 | #2931 | semidirect |
| 123. C2×C8 | D76 | semidirect |
| 160. C4 | #10597347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597347 | 2 |
| #11927094 | 2 |
| #11926623 | 2 |
| C8×D76 | 2 |
| #11926568 | 2 |
| #11926510 | 2 |
| C2×C4×C8×C19 | 2 |
| #2931 | 19 |