Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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×#10597350 | C2 | semidirect |
| 2. #11926976 | C2 | direct (N × H) |
| 3. C2×Dic152 | C2 | semidirect |
| 4. C2×#10597257 | C2 | semidirect |
| 5. C2×D304 | C2 | semidirect |
| 6. C22×C16×C19 | C2 | semidirect |
| 11. #10597350 | C22 | semidirect |
| 16. C2×C16×C19 | C22 | semidirect |
| 17. Dic152 | C22 | semidirect |
| 18. #10597257 | C22 | semidirect |
| 19. D304 | C22 | semidirect |
| 69. C22×C16 | D19 | semidirect |
| 71. C2×C19 | #508 | semidirect |
| 86. C2×C16 | C2×D19 | semidirect |
| 87. C19 | C2×#508 | semidirect |
| 133. C2 | #11926976 | 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 |
| #11926976 | 2 |
| C2×Dic152 | 2 |
| C2×#10597257 | 2 |
| C2×D304 | 2 |
| C22×C16×C19 | 2 |
| C2×#508 | 19 |