Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23750027 | C2 | semidirect |
| 3. #23750026 | C2 | semidirect |
| 4. #23750025 | C2 | semidirect |
| 5. #23750024 | C2 | semidirect |
| 9. #499×C149 | C2 | semidirect |
| 75. D149 | #499 | direct (N × H) |
| 76. C149 | C2×#499 | semidirect |
| 83. #499 | D149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D149 | 2 |
| #23750027 | 2 |
| #23750026 | 2 |
| #23750025 | 2 |
| #23750024 | 2 |
| #107×D149 | 2 |
| #106×D149 | 2 |
| C4×C8×D149 | 2 |
| #499×C149 | 2 |
| C2×#499 | 149 |