Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 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×D596 | C2 | semidirect |
| 2. #23750028 | C2 | semidirect |
| 3. #23749905 | C2 | semidirect |
| 4. #23749902 | C2 | semidirect |
| 5. Q8×#11924746 | C2 | semidirect |
| 7. D4×Q8×C149 | C2 | semidirect |
| 28. #14558721 | Q8 | direct (N × H) |
| 47. D596 | C2×Q8 | semidirect |
| 51. #11924746 | C2×Q8 | semidirect |
| 54. Q8×C149 | D8 | semidirect |
| 56. D4×C149 | C2×Q8 | semidirect |
| 80. C149 | Q8×D8 | semidirect |
| 83. D4×Q8 | D149 | semidirect |
| 129. Q8 | #14558721 | direct (N × H) |
| 133. D4 | 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 |
| #23750028 | 2 |
| #23749905 | 2 |
| #23749902 | 2 |
| Q8×#11924746 | 2 |
| C4×#14558721 | 2 |
| D4×Q8×C149 | 2 |
| Q8×D8 | 149 |