Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750430 | C2 | semidirect |
| 2. #23750061 | C2 | semidirect |
| 3. #23750060 | C2 | semidirect |
| 4. #23750055 | C2 | semidirect |
| 5. C2×#18011852 | C2 | semidirect |
| 6. #23750042 | C2 | semidirect |
| 7. #576×C149 | C2 | semidirect |
| 10. #18011933 | C22 | semidirect |
| 11. C2×D1192 | C22 | semidirect |
| 12. #18011857 | C22 | semidirect |
| 13. #18011855 | C22 | semidirect |
| 14. #18011854 | C22 | semidirect |
| 15. #18011852 | C22 | semidirect |
| 16. #18011852 | C22 | semidirect |
| 17. #18011851 | C22 | semidirect |
| 18. C2×#14558711 | C22 | semidirect |
| 21. #135×C149 | C22 | semidirect |
| 22. C2×D8×C149 | C22 | semidirect |
| 75. C149 | #3415 | semidirect |
| 78. #576 | D149 | semidirect |
| 89. #135 | C2×D149 | semidirect |
| 91. C2×D8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750430 | 2 |
| #23750061 | 2 |
| #23750060 | 2 |
| #23750055 | 2 |
| C2×#18011852 | 2 |
| #23750042 | 2 |
| #576×C149 | 2 |
| #3415 | 149 |