Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #22626992 | C2 | semidirect |
| 3. #22626991 | C2 | semidirect |
| 29. C2×#11924003 | C8 | semidirect |
| 30. C16×D73 | C8 | semidirect |
| 31. C16×D73 | C8 | semidirect |
| 34. C2×C16×C73 | C8 | semidirect |
| 93. C73 | #11999 | semidirect |
| 116. C2×C16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22626992 | 2 |
| #22626991 | 2 |
| C2×#17989474 | 2 |
| #11999 | 73 |