Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#18011870 | C2 | semidirect |
| 3. #23749950 | C2 | direct (N × H) |
| 4. C2×#18011845 | C2 | semidirect |
| 5. C2×#18011843 | C2 | semidirect |
| 6. C2×#18011833 | C2 | semidirect |
| 7. C2×#18011833 | C2 | semidirect |
| 8. C2×C22⋊C8×C149 | C2 | semidirect |
| 14. #18011870 | C22 | semidirect |
| 21. #18011845 | C22 | semidirect |
| 22. #18011843 | C22 | semidirect |
| 23. #18011833 | C22 | semidirect |
| 24. #18011833 | C22 | semidirect |
| 28. C22⋊C8×C149 | C22 | semidirect |
| 109. C2×C149 | #482 | semidirect |
| 114. C149 | C2×#482 | semidirect |
| 123. C2×C22⋊C8 | D149 | semidirect |
| 143. C22⋊C8 | C2×D149 | semidirect |
| 225. C2 | #23749950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011885 | 2 |
| C2×#18011870 | 2 |
| #23749950 | 2 |
| C2×#18011845 | 2 |
| C2×#18011843 | 2 |
| C2×#18011833 | 2 |
| C2×C22⋊C8×C149 | 2 |
| C2×#482 | 149 |