Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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. #22626154 | C2 | semidirect |
| 4. #22626152 | C2 | semidirect |
| 5. #22624986 | C2 | semidirect |
| 6. #22624985 | C2 | semidirect |
| 10. C2×#14556666 | C4 | semidirect |
| 14. C2×#14556664 | C4 | semidirect |
| 16. #17989484 | C4 | semidirect |
| 152. C73 | #12617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989646 | 2 |
| #22626169 | 2 |
| #22626154 | 2 |
| #22626152 | 2 |
| #22624986 | 2 |
| #22624985 | 2 |
| #22609730 | 2 |
| #12617 | 73 |