Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. C2×#17988390 | C2 | semidirect |
| 5. #22610844 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 7. C73×#1387 | C2 | semidirect |
| 12. #17989030 | C4 | semidirect |
| 39. C2×Dic292 | C2×C4 | semidirect |
| 66. M32×C73 | C2×C4 | semidirect |
| 187. #1387 | D73 | semidirect |
| 189. C73 | #13023 | semidirect |
| 238. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989030 | 2 |
| #22618805 | 2 |
| C2×#17988393 | 2 |
| C2×#17988390 | 2 |
| #22610844 | 2 |
| #22608021 | 2 |
| C73×#1387 | 2 |
| #13023 | 73 |