Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D76 | C2 | semidirect |
| 3. #11926896 | C2 | semidirect |
| 4. #11926876 | C2 | semidirect |
| 5. #11926774 | C2 | semidirect |
| 6. #11926750 | C2 | semidirect |
| 7. #11926684 | C2 | semidirect |
| 8. C4×#64527 | C2 | semidirect |
| 9. #11926609 | C2 | semidirect |
| 10. #103×D19 | C2 | semidirect |
| 11. C19×#475 | C2 | semidirect |
| 81. Q8×C19 | #41 | semidirect |
| 94. D76 | SD16 | semidirect |
| 128. #475 | D19 | semidirect |
| 169. C19 | #3298 | semidirect |
| 213. Q8 | #64545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D76 | 2 |
| #11927197 | 2 |
| #11926896 | 2 |
| #11926876 | 2 |
| #11926774 | 2 |
| #11926750 | 2 |
| #11926684 | 2 |
| C4×#64527 | 2 |
| #11926609 | 2 |
| #103×D19 | 2 |
| C19×#475 | 2 |
| #3298 | 19 |