Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #23750353 | C2 | semidirect |
| 3. #23749975 | C2 | semidirect |
| 4. #23749932 | C2 | semidirect |
| 7. #23749832 | C2 | semidirect |
| 8. Q8×#11924746 | C2 | semidirect |
| 9. C4×#14558726 | C2 | semidirect |
| 115. C149 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750353 | 2 |
| #23749979 | 2 |
| #23749975 | 2 |
| #23749932 | 2 |
| #23749905 | 2 |
| #23749844 | 2 |
| #23749832 | 2 |
| Q8×#11924746 | 2 |
| C4×#14558726 | 2 |
| C4×#14558724 | 2 |
| #556×C149 | 2 |
| #3364 | 149 |