Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 15. #17988415 | C4 | semidirect |
| 16. #17988414 | C4 | semidirect |
| 17. #367×C73 | C4 | semidirect |
| 60. #11924003 | C4⋊C4 | semidirect |
| 63. C16×C73 | C4⋊C4 | semidirect |
| 112. C73 | #13167 | semidirect |
| 121. #367 | #64408 | semidirect |
| 170. 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×#17989474 | 2 |
| #22626035 | 2 |
| #22624988 | 2 |
| #367×D73 | 2 |
| #13167 | 73 |