Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14556661 | C2 | semidirect |
| 2. C2×#17989505 | C2 | semidirect |
| 3. #22626159 | C2 | semidirect |
| 4. #22625005 | C2 | semidirect |
| 35. #14556661 | D4 | semidirect |
| 174. C22×C73 | #361 | semidirect |
| 213. C73 | #13004 | semidirect |
| 396. C22 | #17989505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556661 | 2 |
| C2×#17989505 | 2 |
| #22626159 | 2 |
| #22625005 | 2 |
| #466×D73 | 2 |
| #13004 | 73 |