Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 21. #17988415 | C4 | semidirect |
| 22. #17988414 | C4 | semidirect |
| 23. #17988412 | C4 | semidirect |
| 24. #366×C73 | C4 | semidirect |
| 81. #11924003 | C4⋊C4 | semidirect |
| 85. C16×C73 | C4⋊C4 | semidirect |
| 139. C73 | #13174 | semidirect |
| 152. #366 | #64408 | semidirect |
| 217. C16 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989511 | 2 |
| C2×#17989477 | 2 |
| #22626040 | 2 |
| #22626036 | 2 |
| #22625005 | 2 |
| #22625002 | 2 |
| #22611716 | 2 |
| #13174 | 73 |