Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
332 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 3. #22625077 | C2 | semidirect |
| 4. #22625076 | C2 | semidirect |
| 5. #22625061 | C2 | semidirect |
| 6. #22625061 | C2 | semidirect |
| 16. #17989200 | C4 | semidirect |
| 19. #17988959 | C4 | semidirect |
| 25. #17988649 | C4 | semidirect |
| 26. #490×C73 | C4 | semidirect |
| 41. #14556591 | C2×C4 | semidirect |
| 56. C4×#10596831 | C2×C4 | semidirect |
| 58. #125×C73 | C2×C4 | semidirect |
| 61. #97×C73 | C2×C4 | semidirect |
| 171. C73 | #13607 | semidirect |
| 176. #490 | #64408 | semidirect |
| 203. #125 | C2×#64408 | semidirect |
| 224. #97 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626231 | 2 |
| #22626207 | 2 |
| #22625077 | 2 |
| #22625076 | 2 |
| #22625061 | 2 |
| #22621004 | 2 |
| #13607 | 73 |