Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #23750237 | C2 | direct (N × H) |
| 2. C2×#18011911 | C2 | semidirect |
| 4. C2×#18011903 | C2 | semidirect |
| 5. C2×#18011901 | C2 | semidirect |
| 7. C2×C4×Dic298 | C2 | semidirect |
| 10. #18011911 | C22 | semidirect |
| 12. #18011903 | C22 | semidirect |
| 13. #18011901 | C22 | semidirect |
| 15. C4×Dic298 | C22 | semidirect |
| 82. C2×C149 | #541 | semidirect |
| 85. C149 | C2×#541 | semidirect |
| 168. C2 | #23750237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750237 | 2 |
| C2×#18011911 | 2 |
| C2×#18011904 | 2 |
| C2×#18011903 | 2 |
| C2×#18011901 | 2 |
| C2×#18011890 | 2 |
| C2×C4×Dic298 | 2 |
| C2×#117×C149 | 2 |
| C2×#541 | 149 |