Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
734 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22619932 | C2 | semidirect |
| 2. #22619931 | C2 | semidirect |
| 3. #22613210 | C2 | semidirect |
| 4. #22610762 | C2 | semidirect |
| 5. #22608355 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 7. C73×#1486 | C2 | semidirect |
| 39. #14556591 | D4 | semidirect |
| 40. #14556588 | D4 | semidirect |
| 67. C4×#10596831 | D4 | semidirect |
| 84. C4×C8×C73 | D4 | semidirect |
| 121. C4×Dic73 | D8 | semidirect |
| 241. #1486 | D73 | semidirect |
| 243. C73 | #10012 | semidirect |
| 318. C4×C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619932 | 2 |
| #22619931 | 2 |
| #22613210 | 2 |
| #22610762 | 2 |
| #22608355 | 2 |
| #22607759 | 2 |
| C73×#1486 | 2 |
| #10012 | 73 |