Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C4×#14556506 | C2 | semidirect |
| 3. #22607953 | C2 | semidirect |
| 4. #22607929 | C2 | semidirect |
| 5. C73×#1459 | C2 | semidirect |
| 6. C2×#14556579 | C4 | semidirect |
| 9. #17988499 | C4 | semidirect |
| 11. #17988496 | C4 | semidirect |
| 16. #17988455 | C4 | semidirect |
| 200. #1459 | D73 | semidirect |
| 203. C73 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615783 | 2 |
| C4×#14556506 | 2 |
| #22607953 | 2 |
| #22607929 | 2 |
| C73×#1459 | 2 |
| #11730 | 73 |