Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23750033 | C2 | semidirect |
| 3. #23750031 | C2 | semidirect |
| 4. #23750029 | C2 | semidirect |
| 5. #23750027 | C2 | semidirect |
| 6. #23750026 | C2 | semidirect |
| 11. #500×C149 | C2 | semidirect |
| 42. #14558719 | Q8 | semidirect |
| 45. C8×D149 | Q8 | semidirect |
| 107. C149 | #3164 | semidirect |
| 113. #500 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750252 | 2 |
| #23750033 | 2 |
| #23750031 | 2 |
| #23750029 | 2 |
| #23750027 | 2 |
| #23750026 | 2 |
| #23749666 | 2 |
| #23749662 | 2 |
| #107×D149 | 2 |
| #23749579 | 2 |
| #500×C149 | 2 |
| #3164 | 149 |