Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
890 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 140 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. #22626175 | C2 | semidirect |
| 2. C2×#17989486 | C2 | semidirect |
| 3. #22626167 | C2 | semidirect |
| 4. #22626161 | C2 | semidirect |
| 6. C2×#14556665 | C22 | semidirect |
| 7. C2×#14556665 | C22 | semidirect |
| 8. C22×#11924031 | C22 | semidirect |
| 170. C73 | #12685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626175 | 2 |
| C2×#17989486 | 2 |
| #22626167 | 2 |
| #22626161 | 2 |
| #22624644 | 2 |
| #12685 | 73 |