Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 1. #22612213 | C2 | semidirect |
| 2. #22612158 | C2 | semidirect |
| 4. #22609525 | C2 | semidirect |
| 6. C16×#10596831 | C2 | semidirect |
| 68. C16×C73 | SD16 | semidirect |
| 87. #10596831 | SD32 | semidirect |
| 111. C73 | #12505 | semidirect |
| 172. C16 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612213 | 2 |
| #22612158 | 2 |
| #22612154 | 2 |
| #22609525 | 2 |
| #22609520 | 2 |
| C16×#10596831 | 2 |
| C73×#2248 | 2 |
| #12505 | 73 |