Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23750002 | C2 | semidirect |
| 2. #23750001 | C2 | semidirect |
| 3. #23750001 | C2 | semidirect |
| 4. #23749999 | C2 | semidirect |
| 5. #23749973 | C2 | semidirect |
| 6. #23749347 | C2 | semidirect |
| 7. #486×C149 | C2 | semidirect |
| 50. #11924746 | D8 | semidirect |
| 81. C149 | #1721 | semidirect |
| 88. #486 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750002 | 2 |
| #23750001 | 2 |
| #23749999 | 2 |
| #23749973 | 2 |
| #23749347 | 2 |
| #486×C149 | 2 |
| #1721 | 149 |