Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 3. C4×#14556645 | C2 | semidirect |
| 4. #22625143 | C2 | semidirect |
| 5. #22624763 | C2 | semidirect |
| 6. #22624758 | C2 | semidirect |
| 8. Q8×#10596833 | C4 | semidirect |
| 10. #17989615 | C4 | semidirect |
| 25. Q8⋊#10596831 | C4 | semidirect |
| 26. #17988316 | C4 | semidirect |
| 27. #17988314 | C4 | semidirect |
| 28. Q8⋊C8×C73 | C4 | semidirect |
| 117. Q8×C73 | #97 | semidirect |
| 129. D292 | #97 | semidirect |
| 142. #10596833 | #104 | semidirect |
| 179. C73 | #8192 | semidirect |
| 196. Q8⋊C8 | #64408 | semidirect |
| 286. Q8 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626737 | 2 |
| C4×#14556656 | 2 |
| C4×#14556645 | 2 |
| #22625143 | 2 |
| #22624763 | 2 |
| #22624758 | 2 |
| #22608312 | 2 |
| #8192 | 73 |