Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
782 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 320 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. C2×#17989513 | C2 | direct (N × H) |
| 7. #17989513 | C22 | direct (N × H) |
| 9. C22×#11924003 | C4 | semidirect |
| 10. C2×C16×D73 | C4 | semidirect |
| 12. C22×C16×C73 | C4 | semidirect |
| 24. C2×#11924003 | C2×C4 | semidirect |
| 25. C16×D73 | C2×C4 | semidirect |
| 28. C2×C16×C73 | C2×C4 | semidirect |
| 46. #11924003 | C22×C4 | semidirect |
| 50. C16×C73 | C22×C4 | semidirect |
| 71. C22×C73 | #366 | semidirect |
| 73. C2×D73 | #366 | semidirect |
| 84. C2×C73 | C2×#366 | semidirect |
| 86. D73 | C2×#366 | semidirect |
| 92. C73 | C22×#366 | semidirect |
| 98. C22×C16 | #64408 | semidirect |
| 115. C2×C16 | C2×#64408 | semidirect |
| 139. C16 | C22×#64408 | semidirect |
| 165. C22 | #17989513 | direct (N × H) |
| 175. C2 | C2×#17989513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556660 | 2 |
| C2×#17989513 | 2 |
| C22×C16×D73 | 2 |
| C22×#366 | 73 |