Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
502 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22608533 | C2 | semidirect |
| 5. #22607797 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1528 | C2 | semidirect |
| 220. #1528 | D73 | semidirect |
| 223. C73 | #9189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618959 | 2 |
| #22615800 | 2 |
| C4×#14556507 | 2 |
| #22608533 | 2 |
| #22607797 | 2 |
| #22607796 | 2 |
| C73×#1528 | 2 |
| #9189 | 73 |