Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 10. C4×#11924003 | C4 | semidirect |
| 11. C16×Dic73 | C4 | semidirect |
| 12. C4×C16×C73 | C4 | semidirect |
| 42. #11924003 | C4⋊C4 | semidirect |
| 46. C16×C73 | C4⋊C4 | semidirect |
| 68. C4×C73 | #367 | semidirect |
| 71. Dic73 | #367 | semidirect |
| 82. C73 | #12906 | semidirect |
| 91. C4×C16 | #64408 | semidirect |
| 125. C16 | C4⋊#64408 | semidirect |
| 150. C4 | #17989514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989514 | 2 |
| #22625867 | 2 |
| C4×C16×D73 | 2 |
| #12906 | 73 |