Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#17988708 | C2 | semidirect |
| 3. #22611681 | C2 | semidirect |
| 4. #22610825 | C2 | semidirect |
| 5. #22608042 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C73×#2143 | C2 | semidirect |
| 10. #17989028 | C4 | semidirect |
| 12. #17989023 | C4 | semidirect |
| 185. #2143 | D73 | semidirect |
| 189. C73 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| C2×#17988708 | 2 |
| #22611681 | 2 |
| #22610825 | 2 |
| #22608042 | 2 |
| #22608014 | 2 |
| C73×#2143 | 2 |
| #13024 | 73 |