Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
394 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 168 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×#11924753 | C2 | semidirect |
| 2. #23750659 | C2 | semidirect |
| 3. #23750644 | C2 | semidirect |
| 4. #23750629 | C2 | semidirect |
| 46. Q8×C149 | M16 | semidirect |
| 65. C149 | #2991 | semidirect |
| 102. Q8 | #14558746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924753 | 2 |
| #23750659 | 2 |
| #23750644 | 2 |
| #23750629 | 2 |
| C4×#14558737 | 2 |
| #2991 | 149 |