Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597364 | C2 | semidirect |
| 3. Q8×D76 | C2 | semidirect |
| 4. #11926917 | C2 | semidirect |
| 5. #11926791 | C2 | semidirect |
| 6. #11926754 | C2 | semidirect |
| 7. #11926744 | C2 | semidirect |
| 8. #11926709 | C2 | semidirect |
| 9. #11926684 | C2 | semidirect |
| 10. #11926623 | C2 | semidirect |
| 11. C4×Q16×C19 | C2 | semidirect |
| 59. Q16×C19 | D4 | semidirect |
| 127. C4×C19 | #137 | semidirect |
| 141. C4×Q16 | D19 | semidirect |
| 178. C19 | #3278 | semidirect |
| 197. Q16 | D76 | semidirect |
| 265. C4 | #10597364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597364 | 2 |
| #11927216 | 2 |
| Q8×D76 | 2 |
| #11926917 | 2 |
| #11926791 | 2 |
| #11926754 | 2 |
| #11926744 | 2 |
| #11926709 | 2 |
| #11926684 | 2 |
| #11926623 | 2 |
| C4×Q16×C19 | 2 |
| #3278 | 19 |