Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1412 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×C22⋊#64408 | C2 | semidirect |
| 2. #22626071 | C2 | semidirect |
| 3. #22625792 | C2 | semidirect |
| 4. C4×#14556650 | C2 | semidirect |
| 14. C22×#11924029 | C4 | semidirect |
| 18. C2×#14556579 | C4 | semidirect |
| 19. C2×#14556571 | C4 | semidirect |
| 22. C2×C4×Q8×C73 | C4 | semidirect |
| 66. C22⋊#64408 | #41 | semidirect |
| 125. Q8×C73 | #99 | semidirect |
| 187. C73 | #22534 | semidirect |
| 196. C2×C4×Q8 | #64408 | semidirect |
| 303. Q8 | #14556650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊#64408 | 2 |
| #22626071 | 2 |
| #22625792 | 2 |
| C4×#14556650 | 2 |
| C2×#17989249 | 2 |
| #22534 | 73 |