Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×#18011919 | C2 | semidirect |
| 3. #23749702 | C2 | semidirect |
| 4. #23749690 | C2 | semidirect |
| 5. #23749593 | C2 | semidirect |
| 6. C2×C4×#11924746 | C2 | semidirect |
| 7. #423×C149 | C2 | semidirect |
| 34. C2×#11924746 | D4 | semidirect |
| 75. C4×C149 | #131 | semidirect |
| 83. C149 | #2931 | semidirect |
| 89. #423 | D149 | semidirect |
| 160. C4 | #18011919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011919 | 2 |
| #23750175 | 2 |
| #23749702 | 2 |
| #23749690 | 2 |
| #23749593 | 2 |
| C2×C4×#11924746 | 2 |
| #423×C149 | 2 |
| #2931 | 149 |