Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22610476 | C2 | semidirect |
| 4. #22610150 | C2 | semidirect |
| 5. C73×#1392 | C2 | semidirect |
| 135. #1392 | D73 | semidirect |
| 136. C73 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620796 | 2 |
| #22611622 | 2 |
| #22610476 | 2 |
| #22610150 | 2 |
| C73×#1392 | 2 |
| #13429 | 73 |