Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 566 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. #22612810 | C2 | semidirect |
| 4. #22610022 | C2 | semidirect |
| 5. #22607798 | C2 | semidirect |
| 6. #22607777 | C2 | semidirect |
| 12. C2×#14556522 | C4 | semidirect |
| 13. C2×#14556512 | C4 | semidirect |
| 231. C73 | #9261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988903 | 2 |
| #22612810 | 2 |
| #22610768 | 2 |
| #22610022 | 2 |
| #22607798 | 2 |
| #22607777 | 2 |
| C73×#1519 | 2 |
| #9261 | 73 |