Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23749649 | C2 | semidirect |
| 3. C2×#18011839 | C2 | semidirect |
| 4. C43×C149 | C2 | semidirect |
| 7. #18011911 | C4 | semidirect |
| 8. #18011908 | C4 | semidirect |
| 9. #18011899 | C4 | semidirect |
| 36. C42×C149 | D4 | semidirect |
| 63. C4×C149 | #104 | semidirect |
| 72. C149 | #1962 | semidirect |
| 77. C43 | D149 | semidirect |
| 109. C42 | D596 | semidirect |
| 137. C4 | #18011839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23749649 | 2 |
| C2×#18011839 | 2 |
| C43×C149 | 2 |
| #1962 | 149 |