Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10597378 | C2 | semidirect |
| 2. #11927122 | C2 | semidirect |
| 3. C2×#10597294 | C2 | semidirect |
| 4. C2×#10597282 | C2 | semidirect |
| 5. #11926447 | C2 | semidirect |
| 6. #11926312 | C2 | semidirect |
| 7. C2×C19×AGL(1,ℤ/8) | C2 | semidirect |
| 44. C2×D4×C19 | D4 | semidirect |
| 61. M16×C19 | D4 | semidirect |
| 74. #64520 | D4 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D19 | semidirect |
| 183. C19 | #2006 | semidirect |
| 205. C2×D4 | C22⋊D19 | semidirect |
| 218. M16 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597378 | 2 |
| #11927122 | 2 |
| C2×#10597294 | 2 |
| C2×#10597282 | 2 |
| #11926447 | 2 |
| #11926312 | 2 |
| C2×C19×AGL(1,ℤ/8) | 2 |
| #2006 | 19 |