Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. Q8×Dic298 | C2 | semidirect |
| 3. #23750023 | C2 | semidirect |
| 5. #23749911 | C2 | semidirect |
| 7. C8×Q8×C149 | C2 | semidirect |
| 30. #14558725 | Q8 | direct (N × H) |
| 47. Dic298 | C2×Q8 | semidirect |
| 54. Q8×C149 | SD16 | semidirect |
| 59. C8×C149 | C2×Q8 | semidirect |
| 75. C149 | Q8×SD16 | semidirect |
| 82. C8×Q8 | D149 | semidirect |
| 124. Q8 | #14558725 | direct (N × H) |
| 135. C8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic298 | 2 |
| Q8×D596 | 2 |
| #23750023 | 2 |
| #23749916 | 2 |
| #23749911 | 2 |
| C4×#14558725 | 2 |
| C8×Q8×C149 | 2 |
| Q8×SD16 | 149 |