Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22610861 | C2 | semidirect |
| 3. #22608714 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608284 | C2 | semidirect |
| 6. #22607786 | C2 | semidirect |
| 7. C73×#1551 | C2 | semidirect |
| 197. #1551 | D73 | semidirect |
| 201. C73 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620914 | 2 |
| #22610861 | 2 |
| #22608714 | 2 |
| #22608426 | 2 |
| #22608284 | 2 |
| #22607786 | 2 |
| C73×#1551 | 2 |
| #10508 | 73 |