Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #22608221 | C2 | semidirect |
| 5. #22608218 | C2 | semidirect |
| 6. #22607820 | C2 | semidirect |
| 7. C73×#1299 | C2 | semidirect |
| 154. #1299 | D73 | semidirect |
| 155. C73 | #8243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618642 | 2 |
| #22608591 | 2 |
| #22608522 | 2 |
| #22608221 | 2 |
| #22608218 | 2 |
| #22607820 | 2 |
| C73×#1299 | 2 |
| #8243 | 73 |