Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#18011933 | C2 | semidirect |
| 2. #23750136 | C2 | semidirect |
| 3. #23749883 | C2 | semidirect |
| 4. #23749878 | C2 | semidirect |
| 5. #23749871 | C2 | semidirect |
| 6. #23749663 | C2 | semidirect |
| 7. #23749622 | C2 | semidirect |
| 8. C22×M16×C149 | C2 | semidirect |
| 11. C2×Dic596 | C22 | semidirect |
| 12. C2×#14558725 | C22 | semidirect |
| 13. C2×D1192 | C22 | semidirect |
| 20. #18011845 | C22 | semidirect |
| 21. #18011843 | C22 | semidirect |
| 22. #18011836 | C22 | semidirect |
| 23. #18011833 | C22 | semidirect |
| 56. C2×C8×C149 | D4 | semidirect |
| 105. C149 | #3054 | semidirect |
| 108. C22×M16 | D149 | semidirect |
| 156. C2×C8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| #23750136 | 2 |
| #23749883 | 2 |
| #23749878 | 2 |
| #23749871 | 2 |
| #23749663 | 2 |
| #23749622 | 2 |
| C22×M16×C149 | 2 |
| #3054 | 149 |