Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 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. #135×Dic73 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22610817 | C2 | semidirect |
| 5. #22608045 | C2 | semidirect |
| 6. #22608012 | C2 | semidirect |
| 7. C73×#2143 | C2 | semidirect |
| 11. #17989027 | C4 | semidirect |
| 13. #17989022 | C4 | semidirect |
| 34. C2×Dic292 | C2×C4 | semidirect |
| 36. C2×D584 | C2×C4 | semidirect |
| 50. #14556531 | C2×C4 | semidirect |
| 195. #2143 | D73 | semidirect |
| 199. C73 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| #135×Dic73 | 2 |
| #22611668 | 2 |
| #22610817 | 2 |
| #22608045 | 2 |
| #22608012 | 2 |
| C73×#2143 | 2 |
| #13027 | 73 |