Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C2×#10597293 | C2 | semidirect |
| 4. C2×#10597281 | C2 | semidirect |
| 5. #101×D19 | C2 | direct (N × H) |
| 6. C2×C19×#101 | C2 | semidirect |
| 23. C19×#101 | C22 | semidirect |
| 24. #10597293 | C22 | semidirect |
| 25. #10597281 | C22 | semidirect |
| 103. C2×D19 | #101 | direct (N × H) |
| 116. C2×#101 | D19 | direct (N × H) |
| 119. C2×C19 | C2×#101 | semidirect |
| 122. D19 | C2×#101 | direct (N × H) |
| 141. #101 | C2×D19 | direct (N × H) |
| 142. C19 | C22×#101 | semidirect |
| 231. C2 | #101×D19 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D19 | 2 |
| C2×M16×D19 | 2 |
| C2×#10597293 | 2 |
| C2×#10597281 | 2 |
| #101×D19 | 2 |
| C2×C19×#101 | 2 |
| C22×#101 | 19 |