Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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 |
|---|---|---|
| 1. C2×#17989028 | C2 | semidirect |
| 3. #22611865 | C2 | semidirect |
| 4. #22611848 | C2 | semidirect |
| 5. #22611651 | C2 | semidirect |
| 6. #22611542 | C2 | semidirect |
| 7. C23×Q16×C73 | C2 | semidirect |
| 11. C2×#14556537 | C22 | semidirect |
| 12. C2×#14556534 | C22 | semidirect |
| 19. #17988391 | C22 | semidirect |
| 61. C2×Q16×C73 | D4 | semidirect |
| 153. C22×C73 | #510 | semidirect |
| 170. C23×Q16 | D73 | semidirect |
| 177. C73 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D73 | semidirect |
| 325. C22 | #17989028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989028 | 2 |
| #22619512 | 2 |
| #22611865 | 2 |
| #22611848 | 2 |
| #22611651 | 2 |
| #22611542 | 2 |
| C23×Q16×C73 | 2 |
| #33518 | 73 |