Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#18011931 | C2 | semidirect |
| 2. #23750175 | C2 | semidirect |
| 3. #23750007 | C2 | semidirect |
| 4. #23750004 | C2 | semidirect |
| 5. #23750001 | C2 | semidirect |
| 6. #23749999 | C2 | semidirect |
| 7. #23749997 | C2 | semidirect |
| 8. C2×C4×#11924746 | C2 | semidirect |
| 9. #532×C149 | C2 | semidirect |
| 42. C2×#11924746 | D4 | semidirect |
| 93. C4×C149 | #135 | semidirect |
| 101. C149 | #3147 | semidirect |
| 105. #532 | D149 | semidirect |
| 196. C4 | #18011931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011931 | 2 |
| #23750175 | 2 |
| #23750007 | 2 |
| #23750004 | 2 |
| #23750001 | 2 |
| #23749999 | 2 |
| #23749997 | 2 |
| C2×C4×#11924746 | 2 |
| #532×C149 | 2 |
| #3147 | 149 |