Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 26. #14558726 | Q8 | direct (N × H) |
| 51. Q8×C149 | Q16 | semidirect |
| 70. C149 | Q8×Q16 | semidirect |
| 118. Q8 | #14558726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic298 | 2 |
| #23750028 | 2 |
| #23749920 | 2 |
| #23749917 | 2 |
| Q8×#11924746 | 2 |
| C4×#14558726 | 2 |
| Q82×C149 | 2 |
| Q8×Q16 | 149 |