Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627120 | C2 | semidirect |
| 2. C2×#17989688 | C2 | semidirect |
| 3. C2×#17989687 | C2 | semidirect |
| 4. #22627087 | C2 | semidirect |
| 24. #14556686 | D4 | semidirect |
| 146. C73 | #13192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627120 | 2 |
| C2×#17989688 | 2 |
| C2×#17989687 | 2 |
| #22627087 | 2 |
| #22626655 | 2 |
| #13192 | 73 |