Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22611666 | C2 | semidirect |
| 3. #22611647 | C2 | semidirect |
| 4. #22610829 | C2 | semidirect |
| 5. #22608032 | C2 | semidirect |
| 6. #22608017 | C2 | semidirect |
| 7. C73×#2948 | C2 | semidirect |
| 11. C2×#14556535 | C4 | semidirect |
| 12. C2×#14556532 | C4 | semidirect |
| 32. C2×Dic292 | C2×C4 | semidirect |
| 34. C2×D584 | C2×C4 | semidirect |
| 43. C2×#11924003 | C2×C4 | semidirect |
| 175. #2948 | D73 | semidirect |
| 181. C73 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22611666 | 2 |
| #22611647 | 2 |
| #22610829 | 2 |
| #22608032 | 2 |
| #22608017 | 2 |
| C73×#2948 | 2 |
| #13033 | 73 |