Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#14556537 | C2 | semidirect |
| 4. #22612200 | C2 | direct (N × H) |
| 5. C2×#17988363 | C2 | semidirect |
| 6. C2×#494×C73 | C2 | semidirect |
| 12. C2×#14556537 | C22 | semidirect |
| 18. #17988363 | C22 | semidirect |
| 23. #494×C73 | C22 | semidirect |
| 132. C2×C73 | #2251 | semidirect |
| 139. C2×#494 | D73 | semidirect |
| 142. C73 | C2×#2251 | semidirect |
| 158. #494 | C2×D73 | semidirect |
| 268. C2 | #22612200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556537 | 2 |
| C22×#14556534 | 2 |
| C2×#17988971 | 2 |
| #22612200 | 2 |
| C2×#17988363 | 2 |
| C2×#494×C73 | 2 |
| C2×#2251 | 73 |