Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q16×Dic146 | C2 | semidirect |
| 4. #22607988 | C2 | semidirect |
| 5. #22607909 | C2 | semidirect |
| 6. #22607895 | C2 | semidirect |
| 73. Q16×C73 | SD16 | semidirect |
| 103. Dic146 | SD32 | semidirect |
| 135. C73 | #12354 | semidirect |
| 189. Q16 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic146 | 2 |
| #22612154 | 2 |
| #22609288 | 2 |
| #22607988 | 2 |
| #22607909 | 2 |
| #22607895 | 2 |
| C73×#2207 | 2 |
| #12354 | 73 |