Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. #23750355 | C2 | semidirect |
| 3. #23750022 | C2 | semidirect |
| 4. #23750021 | C2 | semidirect |
| 6. #23749911 | C2 | semidirect |
| 7. #23749909 | C2 | semidirect |
| 8. #23749749 | C2 | semidirect |
| 48. #14558724 | Q8 | semidirect |
| 77. Dic298 | SD16 | semidirect |
| 78. Dic298 | C2×Q8 | semidirect |
| 86. #11924746 | C2×Q8 | semidirect |
| 117. C149 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750355 | 2 |
| D4×Dic298 | 2 |
| #23750022 | 2 |
| #23750021 | 2 |
| #23749913 | 2 |
| #23749911 | 2 |
| #23749909 | 2 |
| #23749749 | 2 |
| #23749716 | 2 |
| C4×#14558724 | 2 |
| #476×C149 | 2 |
| Q8×SD16 | 149 |