Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22610136 | C2 | semidirect |
| 5. #22607819 | C2 | semidirect |
| 6. #22607818 | C2 | semidirect |
| 7. C73×#1855 | C2 | semidirect |
| 160. C2×Dic73 | #108 | semidirect |
| 210. #1855 | D73 | semidirect |
| 214. C73 | #8860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618970 | 2 |
| #22610228 | 2 |
| #22610136 | 2 |
| #22608247 | 2 |
| #22607819 | 2 |
| #22607818 | 2 |
| C73×#1855 | 2 |
| #8860 | 73 |