Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 36. C2×#11924003 | Q8 | semidirect |
| 38. #14556527 | Q8 | semidirect |
| 51. M32×C73 | Q8 | semidirect |
| 141. C73 | #13455 | semidirect |
| 172. M32 | Dic146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620471 | 2 |
| C2×#17988412 | 2 |
| #22610714 | 2 |
| #22608040 | 2 |
| #22608026 | 2 |
| #22608021 | 2 |
| C73×#2159 | 2 |
| #13455 | 73 |