Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #23750591 | C2 | semidirect |
| 4. #23750508 | C2 | semidirect |
| 9. C2×#14558745 | C4 | semidirect |
| 11. C22×#11924753 | C4 | semidirect |
| 18. #18011829 | C4 | semidirect |
| 19. #18011828 | C4 | semidirect |
| 20. #100×C149 | C4 | semidirect |
| 77. C149 | #1757 | semidirect |
| 95. #100 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011998 | 2 |
| #23750605 | 2 |
| #23750591 | 2 |
| #23750508 | 2 |
| #23749606 | 2 |
| #1757 | 149 |