Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. C2×#17989692 | C2 | semidirect |
| 3. C2×#17989691 | C2 | semidirect |
| 5. #22627006 | C2 | semidirect |
| 6. #22627006 | C2 | semidirect |
| 165. C2×D73 | #364 | semidirect |
| 191. C73 | #12914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989706 | 2 |
| C2×#17989692 | 2 |
| C2×#17989691 | 2 |
| #22627099 | 2 |
| #22627006 | 2 |
| #22625666 | 2 |
| #12914 | 73 |