Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22608689 | C2 | semidirect |
| 4. #22608612 | C2 | semidirect |
| 6. #22608218 | C2 | semidirect |
| 7. C73×#1997 | C2 | semidirect |
| 131. #10596831 | #100 | semidirect |
| 155. #1997 | D73 | semidirect |
| 161. C73 | #9805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988961 | 2 |
| #22610771 | 2 |
| #22608689 | 2 |
| #22608612 | 2 |
| #22608600 | 2 |
| #22608218 | 2 |
| C73×#1997 | 2 |
| #9805 | 73 |