Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×Dic596 | C2 | semidirect |
| 4. C2×C4×Dic298 | C2 | semidirect |
| 5. #23749848 | C2 | direct (N × H) |
| 6. C2×#18011836 | C2 | semidirect |
| 8. C2×C4⋊C8×C149 | C2 | semidirect |
| 13. C2×Dic596 | C22 | semidirect |
| 19. C4×Dic298 | C22 | semidirect |
| 25. #18011836 | C22 | semidirect |
| 30. C4⋊C8×C149 | C22 | semidirect |
| 110. C2×C149 | #464 | semidirect |
| 115. C149 | C2×#464 | semidirect |
| 122. C2×C4⋊C8 | D149 | semidirect |
| 144. C4⋊C8 | C2×D149 | semidirect |
| 227. C2 | #23749848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic596 | 2 |
| C22×#14558725 | 2 |
| C2×#18011899 | 2 |
| C2×C4×Dic298 | 2 |
| #23749848 | 2 |
| C2×#18011836 | 2 |
| C2×#18011833 | 2 |
| C2×C4⋊C8×C149 | 2 |
| C2×#464 | 149 |