Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#17988365 | C2 | semidirect |
| 5. #22608039 | C2 | semidirect |
| 6. #22608029 | C2 | semidirect |
| 7. C73×#1943 | C2 | semidirect |
| 15. #17988390 | C4 | semidirect |
| 16. #17988387 | C4 | semidirect |
| 153. #1943 | D73 | semidirect |
| 156. C73 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988396 | 2 |
| #22611641 | 2 |
| C2×#17988365 | 2 |
| #22610824 | 2 |
| #22608039 | 2 |
| #22608029 | 2 |
| C73×#1943 | 2 |
| #13153 | 73 |