Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
624 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 170 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. #22626820 | C2 | semidirect |
| 2. #22625552 | C2 | semidirect |
| 3. #22625532 | C2 | semidirect |
| 4. #22625494 | C2 | semidirect |
| 5. #22625291 | C2 | semidirect |
| 6. #22625145 | C2 | semidirect |
| 150. C73 | #17989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626820 | 2 |
| #22625552 | 2 |
| #22625532 | 2 |
| #22625494 | 2 |
| #22625291 | 2 |
| #22625145 | 2 |
| #22620508 | 2 |
| #17989 | 73 |