Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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. #23749703 | C2 | semidirect |
| 2. #23749697 | C2 | semidirect |
| 3. #23749686 | C2 | semidirect |
| 4. #23749592 | C2 | semidirect |
| 5. #23749589 | C2 | semidirect |
| 8. C2×#14558720 | C22 | semidirect |
| 9. C22×#11924746 | C22 | semidirect |
| 10. C4⋊#11924746 | C22 | semidirect |
| 14. C22⋊#11924746 | C22 | semidirect |
| 15. #18011822 | C22 | semidirect |
| 16. C4×#11924746 | C22 | semidirect |
| 89. C149 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749703 | 2 |
| #23749697 | 2 |
| #23749686 | 2 |
| #23749592 | 2 |
| #23749589 | 2 |
| #525×C149 | 2 |
| #2978 | 149 |