Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23750001 | C2 | semidirect |
| 2. #23749820 | C2 | semidirect |
| 3. #23749703 | C2 | semidirect |
| 4. #23749375 | C2 | semidirect |
| 5. #23749369 | C2 | semidirect |
| 6. #23749368 | C2 | semidirect |
| 7. #459×C149 | C2 | semidirect |
| 53. #11924746 | D8 | semidirect |
| 92. C149 | #1687 | semidirect |
| 96. #459 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750001 | 2 |
| #23749820 | 2 |
| #23749703 | 2 |
| #23749375 | 2 |
| #23749369 | 2 |
| #23749368 | 2 |
| #459×C149 | 2 |
| #1687 | 149 |