Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612155 | C2 | semidirect |
| 3. #22612069 | C2 | semidirect |
| 4. #22609325 | C2 | semidirect |
| 5. #22607978 | C2 | semidirect |
| 6. #22607893 | C2 | semidirect |
| 7. C73×Q8⋊C16 | C2 | semidirect |
| 143. Q8⋊C16 | D73 | semidirect |
| 145. C73 | #12380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622906 | 2 |
| #22612155 | 2 |
| #22612069 | 2 |
| #22609325 | 2 |
| #22607978 | 2 |
| #22607893 | 2 |
| C73×Q8⋊C16 | 2 |
| #12380 | 73 |