Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23750035 | C2 | semidirect |
| 4. #23750034 | C2 | semidirect |
| 5. #23750031 | C2 | semidirect |
| 6. #23750029 | C2 | semidirect |
| 7. #23750022 | C2 | semidirect |
| 11. #501×C149 | C2 | semidirect |
| 52. #14558719 | Q8 | semidirect |
| 95. #11924746 | C2×Q8 | semidirect |
| 103. C8×C149 | C2×Q8 | semidirect |
| 124. C149 | #3165 | semidirect |
| 131. #501 | D149 | semidirect |
| 228. C8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750181 | 2 |
| C4⋊Q8×D149 | 2 |
| #23750035 | 2 |
| #23750034 | 2 |
| #23750031 | 2 |
| #23750029 | 2 |
| #23750022 | 2 |
| #23749666 | 2 |
| #23749664 | 2 |
| #23749577 | 2 |
| #501×C149 | 2 |
| #3165 | 149 |