Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22612160 | C2 | semidirect |
| 4. #22609547 | C2 | semidirect |
| 6. #22607850 | C2 | semidirect |
| 7. C73×#2241 | C2 | semidirect |
| 91. #10596831 | SD32 | semidirect |
| 111. #2241 | D73 | semidirect |
| 115. C73 | #12526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612188 | 2 |
| #22612187 | 2 |
| #22612160 | 2 |
| #22609547 | 2 |
| #22609524 | 2 |
| #22607850 | 2 |
| C73×#2241 | 2 |
| #12526 | 73 |