Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23750023 | C2 | semidirect |
| 2. #23749449 | C2 | semidirect |
| 3. #23749446 | C2 | semidirect |
| 20. Q16×C149 | Q8 | semidirect |
| 22. D8×C149 | Q8 | semidirect |
| 52. C149 | #2230 | semidirect |
| 70. Q16 | Dic298 | semidirect |
| 72. D8 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750023 | 2 |
| #23749449 | 2 |
| #23749446 | 2 |
| #23749435 | 2 |
| #443×C149 | 2 |
| #2230 | 149 |