Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #22626352 | C2 | semidirect |
| 2. C2×#17989514 | C2 | semidirect |
| 3. #22625085 | C2 | semidirect |
| 4. #22625084 | C2 | semidirect |
| 7. #17989520 | C22 | semidirect |
| 11. #17989514 | C22 | semidirect |
| 14. #17989019 | C4 | semidirect |
| 18. Q32×D73 | C4 | semidirect |
| 20. D16×D73 | C4 | semidirect |
| 22. #508×C73 | C4 | semidirect |
| 37. Dic584 | C2×C4 | semidirect |
| 42. D1168 | C2×C4 | semidirect |
| 50. Q32×C73 | C2×C4 | semidirect |
| 52. D16×C73 | C2×C4 | semidirect |
| 137. D73 | #1418 | semidirect |
| 143. C73 | C2×#1418 | semidirect |
| 150. #508 | #64408 | semidirect |
| 175. Q32 | C2×#64408 | semidirect |
| 182. D16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626352 | 2 |
| C2×#17989514 | 2 |
| #22625085 | 2 |
| #22625084 | 2 |
| #508×D73 | 2 |
| C2×#1418 | 73 |