Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22610084 | C2 | semidirect |
| 3. #22608632 | C2 | semidirect |
| 5. #22608444 | C2 | semidirect |
| 7. C73×#1290 | C2 | semidirect |
| 164. #1290 | D73 | semidirect |
| 165. C73 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621248 | 2 |
| #22610084 | 2 |
| #22608632 | 2 |
| #22608627 | 2 |
| #22608444 | 2 |
| #22608440 | 2 |
| C73×#1290 | 2 |
| #10514 | 73 |