Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
526 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22626132 | C2 | semidirect |
| 3. C4×#14556660 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 9. #17989499 | C4 | semidirect |
| 15. C4×D584 | C4 | semidirect |
| 16. D8×Dic73 | C4 | semidirect |
| 17. #17988669 | C4 | semidirect |
| 23. C4×D8×C73 | C4 | semidirect |
| 27. #14556664 | C2×C4 | semidirect |
| 30. #14556660 | C2×C4 | semidirect |
| 80. D584 | C42 | semidirect |
| 98. D8×C73 | C42 | semidirect |
| 178. C73 | #12637 | semidirect |
| 187. C4×D8 | #64408 | semidirect |
| 254. D8 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989499 | 2 |
| #22626132 | 2 |
| C4×#14556660 | 2 |
| #22624988 | 2 |
| C4×D8×D73 | 2 |
| #12637 | 73 |