Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23750175 | C2 | semidirect |
| 2. #23750001 | C2 | semidirect |
| 3. #23749971 | C2 | semidirect |
| 4. #23749817 | C2 | semidirect |
| 5. #23749759 | C2 | semidirect |
| 6. #23749678 | C2 | semidirect |
| 7. C2×#127×C149 | C2 | semidirect |
| 9. C2×#14558721 | C22 | semidirect |
| 10. #18011911 | C22 | semidirect |
| 11. #18011908 | C22 | semidirect |
| 16. C4×D596 | C22 | semidirect |
| 17. C4⋊#11924746 | C22 | semidirect |
| 18. #18011832 | C22 | semidirect |
| 20. C4×#11924746 | C22 | semidirect |
| 81. C2×C4×C149 | D8 | semidirect |
| 112. C149 | #3205 | semidirect |
| 115. C2×#127 | D149 | semidirect |
| 193. C2×C4 | #14558721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750001 | 2 |
| #23749971 | 2 |
| #23749817 | 2 |
| #23749759 | 2 |
| #23749678 | 2 |
| C2×#127×C149 | 2 |
| #3205 | 149 |