Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #23749999 | C2 | semidirect |
| 3. #23749975 | C2 | semidirect |
| 4. #23749827 | C2 | semidirect |
| 5. #23749764 | C2 | semidirect |
| 6. #23749678 | C2 | semidirect |
| 7. C2×C4⋊Q8×C149 | C2 | semidirect |
| 73. C2×C4×C149 | SD16 | semidirect |
| 100. C149 | #3206 | semidirect |
| 103. C2×C4⋊Q8 | D149 | semidirect |
| 173. C2×C4 | #14558723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23749999 | 2 |
| #23749975 | 2 |
| #23749827 | 2 |
| #23749764 | 2 |
| #23749678 | 2 |
| C2×C4⋊Q8×C149 | 2 |
| #3206 | 149 |