Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22610850 | C2 | semidirect |
| 3. C4×#14556523 | C2 | semidirect |
| 4. #22608427 | C2 | semidirect |
| 5. C73×#1451 | C2 | semidirect |
| 7. #17988992 | C4 | semidirect |
| 8. #17988964 | C4 | semidirect |
| 9. #17988934 | C4 | semidirect |
| 119. C8×C73 | #104 | semidirect |
| 146. #1451 | D73 | semidirect |
| 147. C73 | #9721 | semidirect |
| 261. C8 | #14556517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620510 | 2 |
| #22610850 | 2 |
| C4×#14556523 | 2 |
| #22608427 | 2 |
| C73×#1451 | 2 |
| #9721 | 73 |