Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22620483 | C2 | semidirect |
| 3. #22619754 | C2 | semidirect |
| 4. #22615876 | C2 | semidirect |
| 5. #22611142 | C2 | semidirect |
| 6. #22610911 | C2 | semidirect |
| 7. #22610143 | C2 | semidirect |
| 8. #22609744 | C2 | semidirect |
| 9. C73×#1965 | C2 | semidirect |
| 134. M16×C73 | #41 | semidirect |
| 206. #1965 | D73 | semidirect |
| 209. C73 | #25690 | semidirect |
| 314. M16 | #11924027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623805 | 2 |
| #22620483 | 2 |
| #22619754 | 2 |
| #22615876 | 2 |
| #22611142 | 2 |
| #22610911 | 2 |
| #22610143 | 2 |
| #22609744 | 2 |
| C73×#1965 | 2 |
| #25690 | 73 |