Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 80 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×#17989520 | C2 | semidirect |
| 2. C2×#17989514 | C2 | semidirect |
| 3. #22625085 | C2 | direct (N × H) |
| 7. #17989520 | C22 | semidirect |
| 10. #17989514 | C22 | semidirect |
| 14. #17989020 | C4 | semidirect |
| 17. C2×D1168 | C4 | semidirect |
| 19. C2×Q32×C73 | C4 | semidirect |
| 35. D1168 | C2×C4 | semidirect |
| 43. Q32×C73 | C2×C4 | semidirect |
| 109. C2×C73 | #1418 | semidirect |
| 118. C73 | C2×#1418 | semidirect |
| 124. C2×Q32 | #64408 | semidirect |
| 145. Q32 | C2×#64408 | semidirect |
| 225. C2 | #22625085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989520 | 2 |
| C2×#17989514 | 2 |
| #22625085 | 2 |
| C2×#17989020 | 2 |
| C2×#1418 | 73 |