Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
280 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #22612160 | C2 | semidirect |
| 4. #22609529 | C2 | semidirect |
| 6. #22607847 | C2 | semidirect |
| 7. C73×#2252 | C2 | semidirect |
| 68. C16×C73 | SD16 | semidirect |
| 104. #2252 | D73 | semidirect |
| 111. C73 | #12508 | semidirect |
| 172. C16 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612187 | 2 |
| #22612160 | 2 |
| #22612156 | 2 |
| #22609529 | 2 |
| #22609524 | 2 |
| #22607847 | 2 |
| C73×#2252 | 2 |
| #12508 | 73 |