Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #22612248 | C2 | semidirect |
| 2. C2×#17988425 | C2 | semidirect |
| 3. #22612056 | C2 | semidirect |
| 4. #22608121 | C2 | semidirect |
| 5. #22608115 | C2 | semidirect |
| 6. #22608073 | C2 | semidirect |
| 8. C2×Dic584 | C22 | semidirect |
| 13. #17988421 | C22 | semidirect |
| 14. C2×#14556497 | C22 | semidirect |
| 15. #17988417 | C22 | semidirect |
| 127. C73 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612248 | 2 |
| C2×#17988425 | 2 |
| #22612056 | 2 |
| #22608121 | 2 |
| #22608115 | 2 |
| #22608073 | 2 |
| C73×#3415 | 2 |
| #13671 | 73 |