Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
582 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22610102 | C2 | semidirect |
| 3. #22608600 | C2 | semidirect |
| 4. #22608599 | C2 | semidirect |
| 5. #22608598 | C2 | semidirect |
| 6. #22608215 | C2 | semidirect |
| 7. C73×#1545 | C2 | semidirect |
| 173. #1545 | D73 | semidirect |
| 175. C73 | #9773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988963 | 2 |
| #22610102 | 2 |
| #22608600 | 2 |
| #22608599 | 2 |
| #22608598 | 2 |
| #22608215 | 2 |
| C73×#1545 | 2 |
| #9773 | 73 |