Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610767 | C2 | semidirect |
| 3. #22610360 | C2 | semidirect |
| 4. #22610357 | C2 | semidirect |
| 5. #22610111 | C2 | semidirect |
| 6. #22607798 | C2 | semidirect |
| 7. C73×#1964 | C2 | semidirect |
| 150. C22⋊C4×C73 | D8 | semidirect |
| 272. #1964 | D73 | semidirect |
| 277. C73 | #10564 | semidirect |
| 420. C22⋊C4 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620679 | 2 |
| #22610767 | 2 |
| #22610360 | 2 |
| #22610357 | 2 |
| #22610111 | 2 |
| #22607798 | 2 |
| C73×#1964 | 2 |
| #10564 | 73 |