Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22607985 | C2 | semidirect |
| 6. #22607980 | C2 | semidirect |
| 7. C73×#1362 | C2 | semidirect |
| 135. #1362 | D73 | semidirect |
| 136. C73 | #11988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620515 | 2 |
| #22611685 | 2 |
| #22608688 | 2 |
| #22607987 | 2 |
| #22607985 | 2 |
| #22607980 | 2 |
| C73×#1362 | 2 |
| #11988 | 73 |