Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
614 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 614 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 |
|---|---|---|
| 1. C22×#14556536 | C2 | semidirect |
| 3. C2×#17988970 | C2 | semidirect |
| 4. C2×#17988390 | C2 | semidirect |
| 5. #22610795 | C2 | semidirect |
| 6. #22608008 | C2 | semidirect |
| 7. C2×#357×C73 | C2 | semidirect |
| 204. C2×#357 | D73 | semidirect |
| 207. C73 | #13326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556536 | 2 |
| C22×#14556532 | 2 |
| C2×#17988970 | 2 |
| C2×#17988390 | 2 |
| #22610795 | 2 |
| #22608008 | 2 |
| C2×#357×C73 | 2 |
| #13326 | 73 |