Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #23750667 | C2 | semidirect |
| 2. #23750553 | C2 | semidirect |
| 3. #23750539 | C2 | semidirect |
| 4. C16×#10597010 | C2 | semidirect |
| 12. Dic1192 | C4 | semidirect |
| 13. #18011855 | C4 | semidirect |
| 15. D16×C149 | C4 | semidirect |
| 49. C149 | #2178 | semidirect |
| 60. D16 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750667 | 2 |
| #23750553 | 2 |
| #23750539 | 2 |
| C16×#10597010 | 2 |
| #23750054 | 2 |
| #2178 | 149 |