Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
674 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 221 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×#17989708 | C2 | semidirect |
| 2. #22627143 | C2 | semidirect |
| 3. #22627121 | C2 | semidirect |
| 4. #22627102 | C2 | semidirect |
| 5. #22627087 | C2 | semidirect |
| 26. #14556686 | D4 | semidirect |
| 120. C73 | #33435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989708 | 2 |
| #22627143 | 2 |
| #22627121 | 2 |
| #22627102 | 2 |
| #22627087 | 2 |
| #22626653 | 2 |
| #33435 | 73 |