Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22610088 | C2 | semidirect |
| 4. #22610059 | C2 | semidirect |
| 5. C73×#1273 | C2 | semidirect |
| 113. #1273 | D73 | semidirect |
| 114. C73 | #10677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610737 | 2 |
| #22610088 | 2 |
| #22610059 | 2 |
| C73×#1273 | 2 |
| #10677 | 73 |