Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22608334 | C2 | semidirect |
| 5. #22607800 | C2 | semidirect |
| 6. #22607794 | C2 | semidirect |
| 7. C73×#1537 | C2 | semidirect |
| 167. #1537 | D73 | semidirect |
| 171. C73 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620938 | 2 |
| #22619009 | 2 |
| #22608627 | 2 |
| #22608334 | 2 |
| #22607800 | 2 |
| #22607794 | 2 |
| C73×#1537 | 2 |
| #9373 | 73 |