Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22608047 | C2 | semidirect |
| 4. #22608011 | C2 | semidirect |
| 5. C73×#3162 | C2 | semidirect |
| 20. C2×Dic292 | Q8 | semidirect |
| 22. C2×D584 | Q8 | semidirect |
| 119. #3162 | D73 | semidirect |
| 124. C73 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611666 | 2 |
| #22610824 | 2 |
| #22608047 | 2 |
| #22608011 | 2 |
| C73×#3162 | 2 |
| #13373 | 73 |