Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22618816 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. C2×#17988398 | C2 | semidirect |
| 5. #22610829 | C2 | semidirect |
| 6. #22608037 | C2 | semidirect |
| 7. C73×#1378 | C2 | semidirect |
| 12. #17989030 | C4 | semidirect |
| 14. #17989025 | C4 | semidirect |
| 39. C2×Dic292 | C2×C4 | semidirect |
| 43. C2×D584 | C2×C4 | semidirect |
| 70. M32×C73 | C2×C4 | semidirect |
| 196. #1378 | D73 | semidirect |
| 197. C73 | #13030 | semidirect |
| 252. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623067 | 2 |
| #22618816 | 2 |
| #22611668 | 2 |
| C2×#17988398 | 2 |
| #22610829 | 2 |
| #22608037 | 2 |
| C73×#1378 | 2 |
| #13030 | 73 |