Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750296 | C2 | semidirect |
| 3. #23749999 | C2 | semidirect |
| 4. #23749856 | C2 | semidirect |
| 5. #23749832 | C2 | semidirect |
| 6. #23749820 | C2 | semidirect |
| 7. #23749785 | C2 | semidirect |
| 8. #23749770 | C2 | semidirect |
| 9. C4×#14558724 | C2 | semidirect |
| 10. D4×#11924746 | C2 | semidirect |
| 11. #547×C149 | C2 | semidirect |
| 52. #14558724 | D4 | semidirect |
| 129. C4×C149 | #135 | semidirect |
| 140. C149 | #3284 | semidirect |
| 144. #547 | D149 | semidirect |
| 272. 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 |
| #23750296 | 2 |
| #23749999 | 2 |
| #23749856 | 2 |
| #23749832 | 2 |
| #23749820 | 2 |
| #23749785 | 2 |
| #23749770 | 2 |
| C4×#14558724 | 2 |
| D4×#11924746 | 2 |
| #547×C149 | 2 |
| #3284 | 149 |