Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1230 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 216 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. #22626214 | C2 | direct (N × H) |
| 3. C2×#17989494 | C2 | semidirect |
| 4. C2×#17989493 | C2 | semidirect |
| 11. #17989494 | C22 | semidirect |
| 12. #17989493 | C22 | semidirect |
| 14. C22×Q8×D73 | C4 | semidirect |
| 16. #17989162 | C4 | semidirect |
| 18. C2×#14556589 | C4 | semidirect |
| 23. C2×#14556548 | C4 | semidirect |
| 24. C2×C4⋊Q8×C73 | C4 | semidirect |
| 43. C2×Q8×D73 | C2×C4 | semidirect |
| 50. #14556589 | C2×C4 | semidirect |
| 62. #14556548 | C2×C4 | semidirect |
| 72. C4⋊Q8×C73 | C2×C4 | semidirect |
| 220. C2×C73 | #2129 | semidirect |
| 230. C73 | C2×#2129 | semidirect |
| 237. C2×C4⋊Q8 | #64408 | semidirect |
| 271. C4⋊Q8 | C2×#64408 | semidirect |
| 447. C2 | #22626214 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989568 | 2 |
| #22626214 | 2 |
| C2×#17989494 | 2 |
| C2×#17989493 | 2 |
| C2×#17989162 | 2 |
| C2×#2129 | 73 |