Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #23749668 | C2 | semidirect |
| 3. #23749667 | C2 | semidirect |
| 6. #23749385 | C2 | semidirect |
| 7. #339×C149 | C2 | semidirect |
| 22. #18011827 | C4 | semidirect |
| 37. #14558720 | C2×C4 | semidirect |
| 51. M16×C149 | C2×C4 | semidirect |
| 114. C149 | #1856 | semidirect |
| 122. #339 | D149 | semidirect |
| 156. M16 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750099 | 2 |
| #23749668 | 2 |
| #23749667 | 2 |
| C2×#18011827 | 2 |
| #23749527 | 2 |
| #23749385 | 2 |
| #339×C149 | 2 |
| #1856 | 149 |