Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #23750703 | C2 | semidirect |
| 2. #23750612 | C2 | semidirect |
| 3. #23750611 | C2 | semidirect |
| 4. D149⋊#100 | C2 | semidirect |
| 5. C2×#18011971 | C2 | semidirect |
| 8. D149⋊M16 | C22 | semidirect |
| 9. C2×#14558745 | C22 | semidirect |
| 10. #18011972 | C22 | semidirect |
| 11. #18011971 | C22 | semidirect |
| 12. #18011971 | C22 | semidirect |
| 131. C149 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750703 | 2 |
| #23750612 | 2 |
| #23750611 | 2 |
| D149⋊#100 | 2 |
| C2×#18011971 | 2 |
| C2×#18011956 | 2 |
| #2888 | 149 |