Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23749755 | C2 | semidirect |
| 4. #23749378 | C2 | semidirect |
| 5. #23749357 | C2 | semidirect |
| 7. #322×C149 | C2 | semidirect |
| 60. C8×C149 | M16 | semidirect |
| 77. C149 | #1592 | semidirect |
| 85. #322 | D149 | semidirect |
| 138. C8 | #14558719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749755 | 2 |
| C4×#14558725 | 2 |
| #23749704 | 2 |
| #23749378 | 2 |
| #23749357 | 2 |
| #23749354 | 2 |
| #322×C149 | 2 |
| #1592 | 149 |