Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#18011918 | C2 | semidirect |
| 3. C2×#18011839 | C2 | semidirect |
| 4. #23749593 | C2 | semidirect |
| 5. #23749389 | C2 | semidirect |
| 6. #23749380 | C2 | semidirect |
| 7. C2×#104×C149 | C2 | semidirect |
| 11. C2×#14558726 | C4 | semidirect |
| 12. C2×#14558724 | C4 | semidirect |
| 13. C2×#14558723 | C4 | semidirect |
| 14. C2×#14558721 | C4 | semidirect |
| 130. C149 | #1876 | semidirect |
| 135. C2×#104 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011931 | 2 |
| C2×#18011918 | 2 |
| C2×#18011839 | 2 |
| #23749593 | 2 |
| #23749389 | 2 |
| #23749380 | 2 |
| C2×#104×C149 | 2 |
| #1876 | 149 |