Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
732 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22610915 | C2 | semidirect |
| 4. #22608450 | C2 | semidirect |
| 5. #22607837 | C2 | semidirect |
| 6. #22607817 | C2 | semidirect |
| 8. C2×#14556621 | C4 | semidirect |
| 14. #17988588 | C4 | semidirect |
| 233. C73 | #9364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619191 | 2 |
| #22610915 | 2 |
| #22609875 | 2 |
| #22608450 | 2 |
| #22607837 | 2 |
| #22607817 | 2 |
| C73×#2341 | 2 |
| #9364 | 73 |