Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23749673 | C2 | semidirect |
| 5. M16×Dic149 | C2 | semidirect |
| 6. #23749384 | C2 | semidirect |
| 7. #344×C149 | C2 | semidirect |
| 16. #18011829 | C4 | semidirect |
| 17. #18011827 | C4 | semidirect |
| 95. C149 | #1932 | semidirect |
| 102. #344 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749673 | 2 |
| #23749643 | 2 |
| C2×#18011837 | 2 |
| #23749607 | 2 |
| M16×Dic149 | 2 |
| #23749384 | 2 |
| #344×C149 | 2 |
| #1932 | 149 |