Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×Dic298 | C2 | semidirect |
| 3. #23750032 | C2 | semidirect |
| 4. #23750030 | C2 | semidirect |
| 5. #23749934 | C2 | semidirect |
| 6. #23749920 | C2 | semidirect |
| 9. #23749755 | C2 | semidirect |
| 63. SD16×C149 | Q8 | semidirect |
| 115. C149 | #3385 | semidirect |
| 165. SD16 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic298 | 2 |
| #23750332 | 2 |
| #23750032 | 2 |
| #23750030 | 2 |
| #23749934 | 2 |
| #23749920 | 2 |
| #23749915 | 2 |
| #23749903 | 2 |
| #23749755 | 2 |
| #23749726 | 2 |
| C4×SD16×C149 | 2 |
| #3385 | 149 |