Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
358 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 9. #17989514 | C4 | semidirect |
| 10. #17989513 | C4 | semidirect |
| 15. #17988363 | C4 | semidirect |
| 16. #17988362 | C4 | semidirect |
| 17. #17988362 | C4 | semidirect |
| 18. #346×C73 | C4 | semidirect |
| 62. #11924003 | C42 | semidirect |
| 67. C16×C73 | C42 | semidirect |
| 115. C73 | #12674 | semidirect |
| 127. #346 | #64408 | semidirect |
| 177. C16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989514 | 2 |
| C2×#17989513 | 2 |
| C4×#14556660 | 2 |
| #22624989 | 2 |
| #346×D73 | 2 |
| #12674 | 73 |