Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23749445 | C2 | semidirect |
| 4. #23749403 | C2 | semidirect |
| 5. #347×C149 | C2 | semidirect |
| 51. C149 | #2165 | semidirect |
| 57. #347 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749577 | 2 |
| #23749445 | 2 |
| #23749406 | 2 |
| #23749403 | 2 |
| #347×C149 | 2 |
| #2165 | 149 |