Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 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. #22618307 | C2 | semidirect |
| 5. #22607791 | C2 | semidirect |
| 6. #22607763 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 25. #14556591 | Q8 | semidirect |
| 28. #14556588 | Q8 | semidirect |
| 176. #1286 | D73 | semidirect |
| 178. C73 | #10362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618307 | 2 |
| #22610758 | 2 |
| #22608492 | 2 |
| #22608490 | 2 |
| #22607791 | 2 |
| #22607763 | 2 |
| C73×#1286 | 2 |
| #10362 | 73 |