Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 2. #22611622 | C2 | semidirect |
| 3. #22610479 | C2 | semidirect |
| 4. #22610476 | C2 | semidirect |
| 5. #22610153 | C2 | semidirect |
| 6. #22608053 | C2 | semidirect |
| 7. C73×#2134 | C2 | semidirect |
| 202. #2134 | D73 | semidirect |
| 207. C73 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620792 | 2 |
| #22611622 | 2 |
| #22610479 | 2 |
| #22610476 | 2 |
| #22610153 | 2 |
| #22608053 | 2 |
| C73×#2134 | 2 |
| #13429 | 73 |