Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
572 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22625830 | C2 | semidirect |
| 2. C2×#17989433 | C2 | semidirect |
| 3. #22624932 | C2 | semidirect |
| 4. #22624913 | C2 | semidirect |
| 205. C73 | #11848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625830 | 2 |
| C2×#17989433 | 2 |
| #22624932 | 2 |
| #22624913 | 2 |
| #22613262 | 2 |
| #11848 | 73 |