Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #23749665 | C2 | semidirect |
| 4. #23749664 | C2 | semidirect |
| 5. #23749663 | C2 | semidirect |
| 6. #23749660 | C2 | semidirect |
| 7. #106×D149 | C2 | semidirect |
| 8. C2×#106×C149 | C2 | semidirect |
| 10. #18011917 | C4 | semidirect |
| 36. #14558720 | C2×C4 | semidirect |
| 37. #14558719 | C2×C4 | semidirect |
| 39. C8×D149 | C2×C4 | semidirect |
| 49. C2×C8×C149 | C2×C4 | semidirect |
| 90. C149 | #2912 | semidirect |
| 99. C2×#106 | D149 | semidirect |
| 133. C2×C8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011917 | 2 |
| #23750106 | 2 |
| #23749665 | 2 |
| #23749664 | 2 |
| #23749663 | 2 |
| #23749660 | 2 |
| #106×D149 | 2 |
| C2×#106×C149 | 2 |
| #2912 | 149 |