Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22626124 | C2 | semidirect |
| 3. #22625446 | C2 | semidirect |
| 5. #22624801 | C2 | semidirect |
| 6. #22624776 | C2 | semidirect |
| 233. C73 | #9249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924037 | 2 |
| #22626124 | 2 |
| #22625446 | 2 |
| #22625256 | 2 |
| #22624801 | 2 |
| #22624776 | 2 |
| C2×#17988875 | 2 |
| #9249 | 73 |