Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#14558736 | C2 | semidirect |
| 2. C2×#18011939 | C2 | semidirect |
| 3. C2×#18011885 | C2 | semidirect |
| 4. #23749772 | C2 | semidirect |
| 5. #23749766 | C2 | semidirect |
| 6. #23749761 | C2 | semidirect |
| 7. #23749627 | C2 | semidirect |
| 8. #407×C149 | C2 | semidirect |
| 13. C2×#14558736 | C22 | semidirect |
| 14. C22×Dic298 | C22 | semidirect |
| 15. C22×D596 | C22 | semidirect |
| 16. C22×D596 | C22 | semidirect |
| 21. C2×#14558725 | C22 | semidirect |
| 22. C2×D1192 | C22 | semidirect |
| 26. #18011885 | C22 | semidirect |
| 27. C2×C4⋊Dic149 | C22 | semidirect |
| 29. #18011836 | C22 | semidirect |
| 30. #18011833 | C22 | semidirect |
| 32. C2×M16×C149 | C22 | semidirect |
| 33. C22⋊C8×C149 | C22 | semidirect |
| 34. C22⋊C8×C149 | C22 | semidirect |
| 42. #14558736 | D4 | semidirect |
| 89. Dic298 | C2×D4 | semidirect |
| 94. D596 | C2×D4 | semidirect |
| 131. C22×C149 | AGL(1,ℤ/8) | semidirect |
| 155. C149 | #3006 | semidirect |
| 164. #407 | D149 | semidirect |
| 180. C2×M16 | C2×D149 | semidirect |
| 189. C22⋊C8 | C2×D149 | semidirect |
| 190. C22⋊C8 | C2×D149 | semidirect |
| 295. C22 | #18011939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558736 | 2 |
| C2×#18011939 | 2 |
| C2×#18011885 | 2 |
| #23749772 | 2 |
| #23749766 | 2 |
| #23749761 | 2 |
| #23749627 | 2 |
| #407×C149 | 2 |
| #3006 | 149 |