Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #22609910 | C2 | semidirect |
| 3. #22609688 | C2 | semidirect |
| 4. #22607755 | C2 | semidirect |
| 5. #22607753 | C2 | semidirect |
| 6. #22607752 | C2 | semidirect |
| 7. C73×#1270 | C2 | semidirect |
| 230. #1270 | D73 | semidirect |
| 231. C73 | #7658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618261 | 2 |
| #22609910 | 2 |
| #22609688 | 2 |
| #22607755 | 2 |
| #22607753 | 2 |
| #22607752 | 2 |
| C73×#1270 | 2 |
| #7658 | 73 |