Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611966 | C2 | semidirect |
| 2. #22609546 | C2 | semidirect |
| 3. #22607995 | C2 | semidirect |
| 4. #22607976 | C2 | semidirect |
| 5. C73×#1589 | C2 | semidirect |
| 77. C8×C73 | D16 | semidirect |
| 100. #1589 | D73 | semidirect |
| 103. C73 | #12491 | semidirect |
| 175. C8 | #14556532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611966 | 2 |
| #22609546 | 2 |
| #22607995 | 2 |
| #22607976 | 2 |
| C73×#1589 | 2 |
| #12491 | 73 |