Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22627125 | C2 | semidirect |
| 2. #22627115 | C2 | semidirect |
| 3. #22627113 | C2 | semidirect |
| 4. #22627109 | C2 | semidirect |
| 5. #22627108 | C2 | semidirect |
| 6. #64408⋊M32 | C2 | semidirect |
| 209. C73 | #13197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627125 | 2 |
| #22627115 | 2 |
| #22627113 | 2 |
| #22627109 | 2 |
| #22627108 | 2 |
| #64408⋊M32 | 2 |
| C2×#17989630 | 2 |
| #13197 | 73 |