Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 53. #11924003 | Q16 | semidirect |
| 63. C16×C73 | Q16 | semidirect |
| 99. C73 | #12524 | semidirect |
| 155. C16 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612213 | 2 |
| #22612211 | 2 |
| #22612204 | 2 |
| #22609548 | 2 |
| #22609540 | 2 |
| #22607847 | 2 |
| C73×#2252 | 2 |
| #12524 | 73 |