Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #22615808 | C2 | semidirect |
| 5. #22608377 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#1534 | C2 | semidirect |
| 193. #1534 | D73 | semidirect |
| 197. C73 | #10021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620334 | 2 |
| #22620054 | 2 |
| #22615808 | 2 |
| #22608479 | 2 |
| #22608377 | 2 |
| #22607797 | 2 |
| C73×#1534 | 2 |
| #10021 | 73 |