Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750029 | C2 | semidirect |
| 3. #23750003 | C2 | semidirect |
| 4. #23749974 | C2 | semidirect |
| 7. Q16×Dic149 | C2 | semidirect |
| 8. #23749719 | C2 | semidirect |
| 9. #23749717 | C2 | semidirect |
| 77. C2×Dic149 | Q16 | semidirect |
| 114. C149 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750177 | 2 |
| #23750029 | 2 |
| #23750003 | 2 |
| #23749974 | 2 |
| #23749866 | 2 |
| #23749864 | 2 |
| Q16×Dic149 | 2 |
| #23749719 | 2 |
| #23749717 | 2 |
| C2×C8×Dic149 | 2 |
| #467×C149 | 2 |
| #3170 | 149 |