Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 7. #17989514 | C4 | direct (N × H) |
| 12. C4×#11924003 | C4 | semidirect |
| 13. C16×Dic73 | C4 | semidirect |
| 14. C16×Dic73 | C4 | semidirect |
| 15. C4×C16×C73 | C4 | semidirect |
| 50. #11924003 | C42 | semidirect |
| 55. C16×C73 | C42 | semidirect |
| 81. C4×C73 | #367 | semidirect |
| 85. Dic73 | #367 | semidirect |
| 96. C73 | C4×#367 | semidirect |
| 106. C4×C16 | #64408 | semidirect |
| 147. C16 | C4×#64408 | semidirect |
| 176. C4 | #17989514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989514 | 2 |
| C4×#14556660 | 2 |
| #22624989 | 2 |
| C4×C16×D73 | 2 |
| C4×#367 | 73 |