Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750295 | C2 | semidirect |
| 2. #23750000 | C2 | semidirect |
| 3. #23749818 | C2 | semidirect |
| 4. #23749817 | C2 | semidirect |
| 5. C8×Dic298 | C2 | semidirect |
| 6. C4×D1192 | C2 | semidirect |
| 7. D8×Dic149 | C2 | semidirect |
| 8. #493×C149 | C2 | semidirect |
| 53. Dic298 | D8 | semidirect |
| 73. C8×C149 | #41 | semidirect |
| 93. C149 | #3391 | semidirect |
| 97. #493 | D149 | semidirect |
| 167. C8 | #14558735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750295 | 2 |
| #23750000 | 2 |
| #23749818 | 2 |
| #23749817 | 2 |
| C8×Dic298 | 2 |
| C4×D1192 | 2 |
| D8×Dic149 | 2 |
| #493×C149 | 2 |
| #3391 | 149 |