Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 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. #23750334 | C2 | semidirect |
| 2. #23750033 | C2 | semidirect |
| 3. #23750027 | C2 | semidirect |
| 4. #23749925 | C2 | semidirect |
| 5. #23749923 | C2 | semidirect |
| 6. #23749903 | C2 | semidirect |
| 7. #23749755 | C2 | semidirect |
| 54. D8×C149 | Q8 | semidirect |
| 96. C149 | #3389 | semidirect |
| 138. D8 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750334 | 2 |
| #23750033 | 2 |
| #23750027 | 2 |
| #23749925 | 2 |
| #23749923 | 2 |
| #23749903 | 2 |
| #23749755 | 2 |
| #23749737 | 2 |
| C4×D8×C149 | 2 |
| #3389 | 149 |