Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750176 | C2 | semidirect |
| 2. #23750002 | C2 | semidirect |
| 3. #23749973 | C2 | semidirect |
| 4. #23749862 | C2 | semidirect |
| 5. #23749707 | C2 | semidirect |
| 6. C4×C8×D149 | C2 | semidirect |
| 7. #500×C149 | C2 | semidirect |
| 58. C4×D149 | D8 | semidirect |
| 65. C8×C149 | #41 | semidirect |
| 85. C149 | #3169 | semidirect |
| 88. #500 | D149 | semidirect |
| 151. C8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| #23750002 | 2 |
| #23749973 | 2 |
| #23749862 | 2 |
| #23749707 | 2 |
| C4×C8×D149 | 2 |
| #500×C149 | 2 |
| #3169 | 149 |