Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22608622 | C2 | semidirect |
| 4. #22608387 | C2 | semidirect |
| 6. #22607805 | C2 | semidirect |
| 7. C73×#1566 | C2 | semidirect |
| 184. #1566 | D73 | semidirect |
| 189. C73 | #10460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619730 | 2 |
| #22609920 | 2 |
| #22608622 | 2 |
| #22608387 | 2 |
| C2×#17988316 | 2 |
| #22607805 | 2 |
| C73×#1566 | 2 |
| #10460 | 73 |