Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22626151 | C2 | semidirect |
| 4. #22626048 | C2 | semidirect |
| 5. #22625011 | C2 | semidirect |
| 6. #22625003 | C2 | semidirect |
| 23. #17988403 | C4 | semidirect |
| 24. #17988401 | C4 | semidirect |
| 25. #17988399 | C4 | semidirect |
| 26. #362×C73 | C4 | semidirect |
| 158. C73 | #13156 | semidirect |
| 170. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989504 | 2 |
| #22626151 | 2 |
| #22626090 | 2 |
| #22626048 | 2 |
| #22625011 | 2 |
| #22625003 | 2 |
| #22611679 | 2 |
| #13156 | 73 |