Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#17988399 | C2 | semidirect |
| 3. #22611666 | C2 | semidirect |
| 4. #22611658 | C2 | semidirect |
| 5. #22611646 | C2 | semidirect |
| 6. #22611536 | C2 | semidirect |
| 7. C73×#1833 | C2 | semidirect |
| 15. #17988971 | C4 | semidirect |
| 16. #17988964 | C4 | semidirect |
| 53. #14556531 | D4 | semidirect |
| 55. C2×#11924003 | D4 | semidirect |
| 181. #1833 | D73 | semidirect |
| 182. C73 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620417 | 2 |
| C2×#17988399 | 2 |
| #22611666 | 2 |
| #22611658 | 2 |
| #22611646 | 2 |
| #22611536 | 2 |
| C73×#1833 | 2 |
| #13215 | 73 |