Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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×#18011976 | C2 | semidirect |
| 2. C2×#18011975 | C2 | semidirect |
| 3. C4×#14558746 | C2 | semidirect |
| 4. C4×C4⋊#10597010 | C2 | semidirect |
| 16. #18011909 | C4 | semidirect |
| 17. #18011907 | C4 | semidirect |
| 18. #18011899 | C4 | semidirect |
| 24. #124×C149 | C4 | semidirect |
| 27. #14558746 | D4 | semidirect |
| 108. Dic149 | #104 | semidirect |
| 117. C149 | #1980 | semidirect |
| 130. #124 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011976 | 2 |
| C2×#18011975 | 2 |
| C4×#14558746 | 2 |
| C4×C4⋊#10597010 | 2 |
| #23750174 | 2 |
| #1980 | 149 |