Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22608828 | C2 | semidirect |
| 4. #22607994 | C2 | semidirect |
| 5. #22607980 | C2 | semidirect |
| 7. C73×#2209 | C2 | semidirect |
| 113. #2209 | D73 | semidirect |
| 120. C73 | #12496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611971 | 2 |
| #22609538 | 2 |
| #22608828 | 2 |
| #22607994 | 2 |
| #22607980 | 2 |
| #22607978 | 2 |
| C73×#2209 | 2 |
| #12496 | 73 |