Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #23750033 | C2 | semidirect |
| 4. #23750032 | C2 | semidirect |
| 5. #23750026 | C2 | semidirect |
| 6. #23750022 | C2 | semidirect |
| 44. C2×#11924746 | Q8 | semidirect |
| 65. M16×C149 | Q8 | semidirect |
| 112. C149 | #3163 | semidirect |
| 159. M16 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750253 | 2 |
| #23750033 | 2 |
| #23750032 | 2 |
| #23750026 | 2 |
| #23750022 | 2 |
| #23749667 | 2 |
| #23749661 | 2 |
| C2×#18011842 | 2 |
| #23749583 | 2 |
| #428×C149 | 2 |
| #3163 | 149 |