Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. C2×#18011903 | C2 | semidirect |
| 3. #23749990 | C2 | direct (N × H) |
| 4. C2×#18011833 | C2 | semidirect |
| 5. C2×#97×C149 | C2 | semidirect |
| 11. #18011903 | C22 | semidirect |
| 14. #18011833 | C22 | semidirect |
| 17. #97×C149 | C22 | semidirect |
| 59. C2×C149 | #490 | semidirect |
| 63. C149 | C2×#490 | semidirect |
| 69. C2×#97 | D149 | semidirect |
| 81. #97 | C2×D149 | semidirect |
| 124. C2 | #23749990 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011908 | 2 |
| C2×#18011903 | 2 |
| #23749990 | 2 |
| C2×#18011833 | 2 |
| C2×#97×C149 | 2 |
| C2×#490 | 149 |