Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#18011933 | C2 | semidirect |
| 2. C2×#18011931 | C2 | semidirect |
| 3. #23750171 | C2 | semidirect |
| 4. #23750018 | C2 | semidirect |
| 5. #23750016 | C2 | semidirect |
| 6. #23750013 | C2 | semidirect |
| 7. #23750011 | C2 | semidirect |
| 8. C2×#18011821 | C2 | semidirect |
| 9. C2×#135×C149 | C2 | semidirect |
| 51. C2×#11924746 | D4 | semidirect |
| 68. C2×C8×C149 | D4 | semidirect |
| 116. C149 | #3150 | semidirect |
| 120. C2×#135 | D149 | semidirect |
| 180. C2×C8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| C2×#18011931 | 2 |
| #23750171 | 2 |
| #23750018 | 2 |
| #23750016 | 2 |
| #23750013 | 2 |
| #23750011 | 2 |
| C2×#18011821 | 2 |
| C2×#135×C149 | 2 |
| #3150 | 149 |