Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22618847 | C2 | semidirect |
| 3. #22611678 | C2 | semidirect |
| 4. C2×#17988399 | C2 | semidirect |
| 5. #22610839 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 12. #17989025 | C4 | semidirect |
| 177. #1388 | D73 | semidirect |
| 179. C73 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989025 | 2 |
| #22618847 | 2 |
| #22611678 | 2 |
| C2×#17988399 | 2 |
| #22610839 | 2 |
| #22608018 | 2 |
| C73×#1388 | 2 |
| #13032 | 73 |