Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#18011944 | C2 | semidirect |
| 2. C2×#18011942 | C2 | semidirect |
| 3. C2×#18011941 | C2 | semidirect |
| 5. C2×#18011909 | C2 | semidirect |
| 6. #23750018 | C2 | semidirect |
| 7. #23750016 | C2 | semidirect |
| 8. #23750003 | C2 | semidirect |
| 9. #23749996 | C2 | semidirect |
| 10. M16×Dic149 | C2 | semidirect |
| 11. C2×#137×C149 | C2 | semidirect |
| 62. #14558720 | D4 | semidirect |
| 86. M16×C149 | D4 | semidirect |
| 140. Dic149 | #137 | semidirect |
| 146. C149 | #3152 | semidirect |
| 151. C2×#137 | D149 | semidirect |
| 224. M16 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011944 | 2 |
| C2×#18011942 | 2 |
| C2×#18011941 | 2 |
| #23750171 | 2 |
| C2×#18011909 | 2 |
| #23750018 | 2 |
| #23750016 | 2 |
| #23750003 | 2 |
| #23749996 | 2 |
| M16×Dic149 | 2 |
| C2×#137×C149 | 2 |
| #3152 | 149 |