Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22610217 | C2 | semidirect |
| 4. #22610151 | C2 | semidirect |
| 5. #22608061 | C2 | semidirect |
| 6. #22608053 | C2 | semidirect |
| 197. C73 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618993 | 2 |
| #22611572 | 2 |
| #22610217 | 2 |
| #22610151 | 2 |
| #22608061 | 2 |
| #22608053 | 2 |
| C73×#1891 | 2 |
| #12963 | 73 |