Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23750023 | C2 | semidirect |
| 3. #23749998 | C2 | semidirect |
| 4. #23749972 | C2 | semidirect |
| 5. #322×C149 | C2 | semidirect |
| 38. C8×C149 | SD16 | semidirect |
| 51. C149 | #1715 | semidirect |
| 57. #322 | D149 | semidirect |
| 90. C8 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750023 | 2 |
| #23750002 | 2 |
| #23749998 | 2 |
| #23749972 | 2 |
| #322×C149 | 2 |
| #1715 | 149 |