Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14558726 | C2 | semidirect |
| 4. #23749881 | C2 | direct (N × H) |
| 5. C2×#18011842 | C2 | semidirect |
| 6. C2×#18011835 | C2 | semidirect |
| 7. C2×#18011834 | C2 | semidirect |
| 11. C2×#14558726 | C22 | semidirect |
| 21. #18011842 | C22 | semidirect |
| 22. #18011835 | C22 | semidirect |
| 23. #18011834 | C22 | semidirect |
| 111. C2×C149 | #470 | semidirect |
| 115. C149 | C2×#470 | semidirect |
| 227. C2 | #23749881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558726 | 2 |
| C22×#14558720 | 2 |
| C2×#18011890 | 2 |
| #23749881 | 2 |
| C2×#18011842 | 2 |
| C2×#18011835 | 2 |
| C2×#18011834 | 2 |
| C2×C22⋊Q8×C149 | 2 |
| C2×#470 | 149 |