Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #11926985 | C2 | direct (N × H) |
| 3. C2×#10597286 | C2 | semidirect |
| 4. C2×#10597285 | C2 | semidirect |
| 5. C2×#10597269 | C2 | semidirect |
| 6. C22×Q16×C19 | C2 | semidirect |
| 12. C2×Q16×C19 | C22 | semidirect |
| 19. #10597286 | C22 | semidirect |
| 20. #10597285 | C22 | semidirect |
| 21. #10597269 | C22 | semidirect |
| 81. C22×Q16 | D19 | semidirect |
| 87. C2×C19 | #510 | semidirect |
| 98. C2×Q16 | C2×D19 | semidirect |
| 106. C19 | C2×#510 | semidirect |
| 165. C2 | #11926985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597350 | 2 |
| #11926985 | 2 |
| C2×#10597286 | 2 |
| C2×#10597285 | 2 |
| C2×#10597269 | 2 |
| C22×Q16×C19 | 2 |
| C2×#510 | 19 |