Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #23750296 | C2 | semidirect |
| 2. D4×Dic298 | C2 | semidirect |
| 3. #23749972 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749905 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. #23749820 | C2 | semidirect |
| 8. #23749818 | C2 | semidirect |
| 9. C8×Dic298 | C2 | semidirect |
| 10. #23749705 | C2 | semidirect |
| 11. C4×D8×C149 | C2 | semidirect |
| 78. Dic298 | D8 | semidirect |
| 96. D4×C149 | #41 | semidirect |
| 131. C149 | #3358 | semidirect |
| 143. C4×D8 | D149 | semidirect |
| 222. D4 | #14558736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750296 | 2 |
| D4×Dic298 | 2 |
| #23749972 | 2 |
| #23749970 | 2 |
| #23749905 | 2 |
| #23749904 | 2 |
| #23749820 | 2 |
| #23749818 | 2 |
| C8×Dic298 | 2 |
| #23749705 | 2 |
| C4×D8×C149 | 2 |
| #3358 | 149 |