Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #22625389 | C2 | semidirect |
| 4. #22625325 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624797 | C2 | semidirect |
| 25. #17988874 | C4 | semidirect |
| 26. #17988797 | C4 | semidirect |
| 27. #17988793 | C4 | semidirect |
| 32. #477×C73 | C4 | semidirect |
| 202. C73 | #9159 | semidirect |
| 206. #477 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626773 | 2 |
| #22625695 | 2 |
| #22625389 | 2 |
| #22625325 | 2 |
| #22624818 | 2 |
| #22624797 | 2 |
| #22620096 | 2 |
| #9159 | 73 |