Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#17989643 | C2 | semidirect |
| 2. C2×#17989484 | C2 | semidirect |
| 3. #22626160 | C2 | semidirect |
| 4. #22624978 | C2 | semidirect |
| 29. #14556665 | D4 | semidirect |
| 171. C2×D73 | #349 | semidirect |
| 193. C73 | #12985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989643 | 2 |
| C2×#17989484 | 2 |
| #22626160 | 2 |
| #22624978 | 2 |
| C2×#17988657 | 2 |
| #12985 | 73 |