Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1046 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1046 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#17988737 | C2 | semidirect |
| 3. C2×#17988324 | C2 | semidirect |
| 4. C2×#17988321 | C2 | semidirect |
| 5. #22608171 | C2 | semidirect |
| 6. #22607774 | C2 | semidirect |
| 7. C73×#2639 | C2 | semidirect |
| 281. #2639 | D73 | semidirect |
| 286. C73 | #9963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988737 | 2 |
| C2×#17988720 | 2 |
| C2×#17988324 | 2 |
| C2×#17988321 | 2 |
| #22608171 | 2 |
| #22607774 | 2 |
| C73×#2639 | 2 |
| #9963 | 73 |