Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22618732 | C2 | semidirect |
| 3. #22611648 | C2 | semidirect |
| 4. #22610805 | C2 | semidirect |
| 5. #22608038 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C2×#360×C73 | C2 | semidirect |
| 11. #17989022 | C4 | semidirect |
| 34. C2×D584 | C2×C4 | semidirect |
| 47. #14556531 | C2×C4 | semidirect |
| 108. Q16×C73 | C22⋊C4 | semidirect |
| 112. D8×C73 | C22⋊C4 | semidirect |
| 187. C2×#360 | D73 | semidirect |
| 192. C73 | #13025 | semidirect |
| 276. Q16 | #11924005 | semidirect |
| 284. D8 | #11924005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989022 | 2 |
| #22618732 | 2 |
| #22611648 | 2 |
| #22610805 | 2 |
| #22608038 | 2 |
| #22608014 | 2 |
| C2×#360×C73 | 2 |
| #13025 | 73 |