Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22610484 | C2 | semidirect |
| 5. #22610153 | C2 | semidirect |
| 6. #22608053 | C2 | semidirect |
| 7. C73×#2135 | C2 | semidirect |
| 194. #2135 | D73 | semidirect |
| 200. C73 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620798 | 2 |
| #22611622 | 2 |
| #22610484 | 2 |
| #22610476 | 2 |
| #22610153 | 2 |
| #22608053 | 2 |
| C73×#2135 | 2 |
| #13430 | 73 |