Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22607987 | C2 | semidirect |
| 5. #22607986 | C2 | semidirect |
| 6. #22607985 | C2 | semidirect |
| 7. C73×#1364 | C2 | semidirect |
| 134. #1364 | D73 | semidirect |
| 135. C73 | #11974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D73 | 2 |
| #22611733 | 2 |
| #22608693 | 2 |
| #22607987 | 2 |
| #22607986 | 2 |
| #22607985 | 2 |
| C73×#1364 | 2 |
| #11974 | 73 |