Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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. #22612212 | C2 | direct (N × H) |
| 27. C2×#11924003 | Q8 | semidirect |
| 36. C2×C16×C73 | Q8 | semidirect |
| 51. #11924003 | C2×Q8 | semidirect |
| 60. C16×C73 | C2×Q8 | semidirect |
| 87. C2×C73 | #2254 | semidirect |
| 96. C73 | C2×#2254 | semidirect |
| 121. C2×C16 | Dic146 | semidirect |
| 150. C16 | C2×Dic146 | semidirect |
| 176. C2 | #22612212 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988991 | 2 |
| #22612212 | 2 |
| C2×#17988415 | 2 |
| C2×#17988414 | 2 |
| C2×C16×Dic73 | 2 |
| C2×#367×C73 | 2 |
| C2×#2254 | 73 |