Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#14556660 | C2 | semidirect |
| 3. #22625490 | C2 | semidirect |
| 4. #22624828 | C2 | semidirect |
| 15. Q8×#10596831 | C4 | semidirect |
| 17. C8×D292 | C4 | semidirect |
| 19. #17988652 | C4 | semidirect |
| 24. C8×Q8×C73 | C4 | semidirect |
| 113. Q8×C73 | #107 | semidirect |
| 126. D292 | #107 | semidirect |
| 145. #10596831 | #104 | semidirect |
| 179. C73 | #8667 | semidirect |
| 182. C8×Q8 | #64408 | semidirect |
| 284. Q8 | #14556660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625804 | 2 |
| C4×#14556660 | 2 |
| #22625490 | 2 |
| #22624828 | 2 |
| C8×#11924029 | 2 |
| #8667 | 73 |