Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22608352 | C2 | semidirect |
| 5. #22607769 | C2 | semidirect |
| 6. #22607767 | C2 | semidirect |
| 7. C73×#1485 | C2 | semidirect |
| 186. #1485 | D73 | semidirect |
| 189. C73 | #9067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620256 | 2 |
| #22618997 | 2 |
| #22608522 | 2 |
| #22608352 | 2 |
| #22607769 | 2 |
| #22607767 | 2 |
| C73×#1485 | 2 |
| #9067 | 73 |