Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D149 | C2 | semidirect |
| 3. #23749940 | C2 | semidirect |
| 4. #23749917 | C2 | semidirect |
| 5. #23749826 | C2 | semidirect |
| 6. #23749825 | C2 | semidirect |
| 7. #23749765 | C2 | semidirect |
| 8. #23749728 | C2 | semidirect |
| 9. #23749724 | C2 | semidirect |
| 10. #23749681 | C2 | semidirect |
| 11. #477×C149 | C2 | semidirect |
| 87. Dic298 | #41 | semidirect |
| 108. Q8×C149 | #41 | semidirect |
| 140. C149 | #3112 | semidirect |
| 146. #477 | D149 | semidirect |
| 231. Q8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| C4×Q8×D149 | 2 |
| #23749940 | 2 |
| #23749917 | 2 |
| #23749826 | 2 |
| #23749825 | 2 |
| #23749765 | 2 |
| #23749728 | 2 |
| #23749724 | 2 |
| #23749681 | 2 |
| #477×C149 | 2 |
| #3112 | 149 |