Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22620853 | C2 | semidirect |
| 2. #22614884 | C2 | semidirect |
| 3. #22608613 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608322 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 110. C2×D4×C73 | SD16 | semidirect |
| 224. C73 | #10240 | semidirect |
| 313. C2×D4 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620853 | 2 |
| #22614884 | 2 |
| #22608613 | 2 |
| #22608426 | 2 |
| #22608322 | 2 |
| #22607832 | 2 |
| C73×#3036 | 2 |
| #10240 | 73 |