Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
998 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22625795 | C2 | semidirect |
| 2. #22625444 | C2 | semidirect |
| 3. #22625256 | C2 | semidirect |
| 4. #22625170 | C2 | semidirect |
| 164. D4×C73 | #100 | semidirect |
| 244. C73 | #8393 | semidirect |
| 408. D4 | #14556651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625795 | 2 |
| #22625444 | 2 |
| #22625256 | 2 |
| #22625170 | 2 |
| C2×#17989236 | 2 |
| #8393 | 73 |