Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11926906 | C2 | direct (N × H) |
| 3. C2×#10597267 | C2 | semidirect |
| 5. C2×#10597260 | C2 | semidirect |
| 6. C2×C19×C4⋊Q8 | C2 | semidirect |
| 11. C19×C4⋊Q8 | C22 | semidirect |
| 20. #10597267 | C22 | semidirect |
| 22. #10597260 | C22 | semidirect |
| 83. C2×C4⋊Q8 | D19 | semidirect |
| 89. C2×C19 | #489 | semidirect |
| 99. C4⋊Q8 | C2×D19 | semidirect |
| 110. C19 | C2×#489 | semidirect |
| 171. C2 | #11926906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597321 | 2 |
| #11926906 | 2 |
| C2×#10597267 | 2 |
| C2×#10597266 | 2 |
| C2×#10597260 | 2 |
| C2×C19×C4⋊Q8 | 2 |
| C2×#489 | 19 |