Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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. #17988427 | C4 | semidirect |
| 89. C73 | #13653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988427 | 2 |
| C4×Dic584 | 2 |
| #22608132 | 2 |
| #22608112 | 2 |
| #22608111 | 2 |
| #22608065 | 2 |
| C4×Q32×C73 | 2 |
| #13653 | 73 |