Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22626951 | C2 | semidirect |
| 4. #22626950 | C2 | semidirect |
| 27. #14556664 | C8 | semidirect |
| 30. C2×#11924031 | C8 | semidirect |
| 36. C2×#11924003 | C8 | semidirect |
| 37. C16×D73 | C8 | semidirect |
| 38. C16×D73 | C8 | semidirect |
| 41. C2×C16×C73 | C8 | semidirect |
| 102. C73 | #11405 | semidirect |
| 131. C2×C16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| #22627040 | 2 |
| #22626951 | 2 |
| #22626950 | 2 |
| C2×#17989474 | 2 |
| #11405 | 73 |