Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
922 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22610870 | C2 | semidirect |
| 3. #22608624 | C2 | semidirect |
| 4. #22608543 | C2 | semidirect |
| 5. #22608542 | C2 | semidirect |
| 6. #22608274 | C2 | semidirect |
| 7. C73×#1551 | C2 | semidirect |
| 228. #1551 | D73 | semidirect |
| 232. C73 | #8459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623697 | 2 |
| #22610870 | 2 |
| #22608624 | 2 |
| #22608543 | 2 |
| #22608542 | 2 |
| #22608274 | 2 |
| C73×#1551 | 2 |
| #8459 | 73 |