Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750035 | C2 | semidirect |
| 3. #23750028 | C2 | semidirect |
| 5. #23749920 | C2 | semidirect |
| 6. #23749910 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 11. #557×C149 | C2 | semidirect |
| 47. #14558723 | Q8 | semidirect |
| 84. #11924746 | C2×Q8 | semidirect |
| 88. Q8×C149 | C2×Q8 | semidirect |
| 116. C149 | #3386 | semidirect |
| 118. #557 | D149 | semidirect |
| 196. Q8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D596 | 2 |
| #23750035 | 2 |
| #23750028 | 2 |
| #23749922 | 2 |
| #23749920 | 2 |
| #23749910 | 2 |
| #23749902 | 2 |
| #23749756 | 2 |
| #23749723 | 2 |
| C4×#14558723 | 2 |
| #557×C149 | 2 |
| #3386 | 149 |