Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22620934 | C2 | semidirect |
| 2. #22620305 | C2 | semidirect |
| 3. #22608645 | C2 | semidirect |
| 4. #22608529 | C2 | semidirect |
| 5. #22608442 | C2 | semidirect |
| 6. #22607824 | C2 | semidirect |
| 34. #14556591 | D4 | semidirect |
| 35. #14556591 | D4 | semidirect |
| 43. C4⋊#10596831 | D4 | semidirect |
| 52. #14556502 | D4 | semidirect |
| 208. C73 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620934 | 2 |
| #22620305 | 2 |
| #22608645 | 2 |
| #22608529 | 2 |
| #22608442 | 2 |
| #22607824 | 2 |
| C73×#2657 | 2 |
| #10096 | 73 |