Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #23749580 | C2 | semidirect |
| 5. #23749390 | C2 | semidirect |
| 6. #23749385 | C2 | semidirect |
| 7. C2×C4×C8×C149 | C2 | semidirect |
| 10. #18011917 | C4 | semidirect |
| 16. #18011839 | C4 | semidirect |
| 17. #18011836 | C4 | semidirect |
| 18. #18011833 | C4 | semidirect |
| 98. C149 | #1764 | semidirect |
| 104. C2×C4×C8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011917 | 2 |
| C2×#18011839 | 2 |
| #23749622 | 2 |
| #23749580 | 2 |
| #23749390 | 2 |
| #23749385 | 2 |
| C2×C4×C8×C149 | 2 |
| #1764 | 149 |