Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23750391 | C2 | semidirect |
| 3. #23749643 | C2 | semidirect |
| 4. #23749629 | C2 | semidirect |
| 5. C2×#18011827 | C2 | semidirect |
| 6. #23749383 | C2 | semidirect |
| 7. #344×C149 | C2 | semidirect |
| 12. C2×#14558725 | C4 | semidirect |
| 13. C2×D1192 | C4 | semidirect |
| 112. C149 | #1903 | semidirect |
| 119. #344 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011939 | 2 |
| #23750391 | 2 |
| #23749643 | 2 |
| #23749629 | 2 |
| C2×#18011827 | 2 |
| #23749383 | 2 |
| #344×C149 | 2 |
| #1903 | 149 |