Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 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. #22611639 | C2 | semidirect |
| 4. #22610830 | C2 | semidirect |
| 5. #22608045 | C2 | semidirect |
| 6. #22608019 | C2 | semidirect |
| 7. C2×#359×C73 | C2 | semidirect |
| 10. #17989028 | C4 | semidirect |
| 12. #17989023 | C4 | semidirect |
| 183. C2×#359 | D73 | semidirect |
| 188. C73 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| #22618847 | 2 |
| #22611639 | 2 |
| #22610830 | 2 |
| #22608045 | 2 |
| #22608019 | 2 |
| C2×#359×C73 | 2 |
| #13021 | 73 |