Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 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×#18011885 | C2 | semidirect |
| 2. #23749939 | C2 | semidirect |
| 3. #23749861 | C2 | semidirect |
| 4. #23749761 | C2 | semidirect |
| 5. C2×C22⋊C8×C149 | C2 | semidirect |
| 6. C22×D596 | C22 | semidirect |
| 8. C2×D1192 | C22 | semidirect |
| 12. #18011885 | C22 | semidirect |
| 13. C2×C4⋊Dic149 | C22 | semidirect |
| 15. #18011845 | C22 | semidirect |
| 16. #18011833 | C22 | semidirect |
| 18. C22×C8×C149 | C22 | semidirect |
| 19. C22⋊C8×C149 | C22 | semidirect |
| 53. C23×C149 | D8 | semidirect |
| 86. C149 | #3186 | semidirect |
| 92. C2×C22⋊C8 | D149 | semidirect |
| 97. C22×C8 | C2×D149 | semidirect |
| 106. C22⋊C8 | C2×D149 | semidirect |
| 134. C23 | D1192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011885 | 2 |
| #23749939 | 2 |
| #23749861 | 2 |
| #23749761 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #3186 | 149 |