Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#17988411 | C2 | semidirect |
| 5. #22610712 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 7. C73×#1385 | C2 | semidirect |
| 19. #17988393 | C4 | semidirect |
| 149. #1385 | D73 | semidirect |
| 151. C73 | #12948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618847 | 2 |
| C2×#17988411 | 2 |
| C2×#17988398 | 2 |
| #22611658 | 2 |
| #22610712 | 2 |
| #22608018 | 2 |
| C73×#1385 | 2 |
| #12948 | 73 |