Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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×#17989020 | C2 | semidirect |
| 2. #22621690 | C2 | semidirect |
| 3. #22612181 | C2 | semidirect |
| 4. #22612018 | C2 | semidirect |
| 5. #22611971 | C2 | semidirect |
| 6. #22611857 | C2 | semidirect |
| 7. C16×D292 | C2 | semidirect |
| 8. C4×Q32×C73 | C2 | semidirect |
| 52. Q32×C73 | D4 | semidirect |
| 124. C4×C73 | #508 | semidirect |
| 140. C4×Q32 | D73 | semidirect |
| 142. C73 | #33853 | semidirect |
| 178. Q32 | D292 | semidirect |
| 259. C4 | #17989020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989020 | 2 |
| #22621690 | 2 |
| #22612181 | 2 |
| #22612018 | 2 |
| #22611971 | 2 |
| #22611857 | 2 |
| C16×D292 | 2 |
| C4×Q32×C73 | 2 |
| #33853 | 73 |