Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22608533 | C2 | semidirect |
| 5. #22607800 | C2 | semidirect |
| 6. #22607780 | C2 | semidirect |
| 7. C73×#1470 | C2 | semidirect |
| 208. #1470 | D73 | semidirect |
| 211. C73 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988884 | 2 |
| #22618965 | 2 |
| #22608533 | 2 |
| #22608373 | 2 |
| #22607800 | 2 |
| #22607780 | 2 |
| C73×#1470 | 2 |
| #9245 | 73 |