Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 200 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. #23750684 | C2 | semidirect |
| 2. #23750683 | C2 | semidirect |
| 3. D149⋊M32 | C2 | semidirect |
| 4. C2×D149⋊C16 | C2 | semidirect |
| 6. #18011986 | C22 | semidirect |
| 7. #18011985 | C22 | semidirect |
| 10. D149⋊C16 | C22 | semidirect |
| 11. C2×#14558739 | C22 | semidirect |
| 64. D149 | #504 | semidirect |
| 65. C149 | C2×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750684 | 2 |
| #23750683 | 2 |
| D149⋊M32 | 2 |
| C2×D149⋊C16 | 2 |
| #131×D149 | 2 |
| C2×#504 | 149 |