Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23750279 | C2 | semidirect |
| 2. #23750028 | C2 | semidirect |
| 3. #23749938 | C2 | semidirect |
| 4. #23749936 | C2 | semidirect |
| 5. #23749905 | C2 | semidirect |
| 6. #23749902 | C2 | semidirect |
| 7. #23749859 | C2 | semidirect |
| 8. C4×#14558721 | C2 | semidirect |
| 9. D4×#11924746 | C2 | semidirect |
| 10. C2×#18011844 | C2 | semidirect |
| 11. #547×C149 | C2 | semidirect |
| 86. #11924746 | #41 | semidirect |
| 93. D4×C149 | D8 | semidirect |
| 129. C149 | #3334 | semidirect |
| 132. #547 | D149 | semidirect |
| 216. D4 | #14558721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750279 | 2 |
| #23750028 | 2 |
| #23749938 | 2 |
| #23749936 | 2 |
| #23749905 | 2 |
| #23749902 | 2 |
| #23749859 | 2 |
| C4×#14558721 | 2 |
| D4×#11924746 | 2 |
| C2×#18011844 | 2 |
| #547×C149 | 2 |
| #3334 | 149 |