Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1080 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 274 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. #22626052 | C2 | semidirect |
| 2. #22626000 | C2 | semidirect |
| 3. #22625904 | C2 | semidirect |
| 4. #22625753 | C2 | semidirect |
| 6. C23×#10596833 | C22 | semidirect |
| 7. C2×C4⋊#10596833 | C22 | semidirect |
| 10. C2×C22⋊#10596833 | C22 | semidirect |
| 11. C2×C4×#10596833 | C22 | semidirect |
| 12. #17989453 | C22 | semidirect |
| 43. #120×C73 | C8 | semidirect |
| 72. C24×C73 | C2×C8 | semidirect |
| 79. C22⋊C4×C73 | C2×C8 | semidirect |
| 140. C73 | #23306 | semidirect |
| 165. #120 | #10596833 | semidirect |
| 182. C24 | C2×#10596833 | semidirect |
| 212. C22⋊C4 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626052 | 2 |
| #22626000 | 2 |
| #22625904 | 2 |
| #22625753 | 2 |
| #120×Dic73 | 2 |
| #23306 | 73 |