Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750360 | C2 | semidirect |
| 2. #23750007 | C2 | semidirect |
| 3. #23749999 | C2 | semidirect |
| 4. #23749847 | C2 | semidirect |
| 5. #23749837 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 8. Q8×#11924746 | C2 | semidirect |
| 9. C4×#14558723 | C2 | semidirect |
| 10. C4×#14558724 | C2 | semidirect |
| 11. #556×C149 | C2 | semidirect |
| 125. C149 | #3394 | semidirect |
| 128. #556 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750360 | 2 |
| #23750007 | 2 |
| #23749999 | 2 |
| #23749847 | 2 |
| #23749837 | 2 |
| #23749832 | 2 |
| #23749820 | 2 |
| Q8×#11924746 | 2 |
| C4×#14558723 | 2 |
| C4×#14558724 | 2 |
| #556×C149 | 2 |
| #3394 | 149 |