Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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. C2×#10597388 | C2 | semidirect |
| 3. #11927118 | C2 | semidirect |
| 4. #11926705 | C2 | semidirect |
| 5. #11926698 | C2 | semidirect |
| 6. #11926553 | C2 | semidirect |
| 7. #11926541 | C2 | semidirect |
| 8. #11926510 | C2 | semidirect |
| 9. C22×Q16×C19 | C2 | semidirect |
| 138. C22×Q16 | D19 | semidirect |
| 177. C19 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597433 | 2 |
| C2×#10597388 | 2 |
| #11927118 | 2 |
| #11926705 | 2 |
| #11926698 | 2 |
| #11926553 | 2 |
| #11926541 | 2 |
| #11926510 | 2 |
| C22×Q16×C19 | 2 |
| #3011 | 19 |