Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 128 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. #17989513 | C4 | semidirect |
| 11. C16×#64408 | C4 | semidirect |
| 15. #17988413 | C4 | semidirect |
| 16. #17988412 | C4 | semidirect |
| 17. #366×C73 | C4 | semidirect |
| 60. #11924003 | C42 | semidirect |
| 63. C16×C73 | C42 | semidirect |
| 98. #64408 | #366 | direct (N × H) |
| 118. C73 | C4×#366 | semidirect |
| 128. #366 | #64408 | direct (N × H) |
| 176. C16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989513 | 2 |
| C2×C16×#64408 | 2 |
| #107×#64408 | 2 |
| #22624988 | 2 |
| #366×D73 | 2 |
| C4×#366 | 73 |