Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#18011981 | C2 | semidirect |
| 2. #23750635 | C2 | semidirect |
| 4. #23750508 | C2 | semidirect |
| 16. #18011919 | C4 | semidirect |
| 17. #18011918 | C4 | semidirect |
| 19. #18011917 | C4 | semidirect |
| 24. #131×C149 | C4 | semidirect |
| 111. C149 | #1814 | semidirect |
| 124. #131 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011981 | 2 |
| #23750635 | 2 |
| #23750622 | 2 |
| #23750508 | 2 |
| #131×D149 | 2 |
| #1814 | 149 |