Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
992 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×D149⋊M16 | C2 | semidirect |
| 2. D149⋊#100 | C2 | direct (N × H) |
| 3. C2×#18011971 | C2 | semidirect |
| 7. D149⋊M16 | C22 | semidirect |
| 8. C2×#14558745 | C22 | semidirect |
| 10. #18011971 | C22 | semidirect |
| 23. #14558745 | C23 | semidirect |
| 108. C2×D149 | #100 | semidirect |
| 117. C2×C149 | C2×#100 | semidirect |
| 121. D149 | C2×#100 | semidirect |
| 122. C149 | C22×#100 | semidirect |
| 243. C2 | D149⋊#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D149⋊M16 | 2 |
| D149⋊#100 | 2 |
| C2×#18011971 | 2 |
| C22×D4×D149 | 2 |
| C22×#100 | 149 |