Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22607994 | C2 | semidirect |
| 4. Q8⋊#11924003 | C2 | semidirect |
| 6. #22607847 | C2 | semidirect |
| 7. C73×#2183 | C2 | semidirect |
| 67. C16×C73 | SD16 | semidirect |
| 106. #2183 | D73 | semidirect |
| 113. C73 | #12049 | semidirect |
| 173. C16 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D292 | 2 |
| C8×#11924015 | 2 |
| #22607994 | 2 |
| Q8⋊#11924003 | 2 |
| #22607885 | 2 |
| #22607847 | 2 |
| C73×#2183 | 2 |
| #12049 | 73 |