Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#18011910 | C2 | semidirect |
| 3. #23749919 | C2 | semidirect |
| 4. #23749914 | C2 | semidirect |
| 5. #23749909 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. #23749668 | C2 | semidirect |
| 8. #23749648 | C2 | semidirect |
| 11. #428×C149 | C2 | semidirect |
| 44. #14558736 | Q8 | semidirect |
| 87. Dic298 | C2×Q8 | semidirect |
| 89. D596 | C2×Q8 | semidirect |
| 138. C149 | #3079 | semidirect |
| 147. #428 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011910 | 2 |
| #23750093 | 2 |
| #23749919 | 2 |
| #23749914 | 2 |
| #23749909 | 2 |
| #23749904 | 2 |
| #23749668 | 2 |
| #23749648 | 2 |
| #23749627 | 2 |
| #23749624 | 2 |
| #428×C149 | 2 |
| #3079 | 149 |