Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #22626132 | C2 | semidirect |
| 2. #22625473 | C2 | semidirect |
| 3. #22624890 | C2 | semidirect |
| 4. #22624889 | C2 | semidirect |
| 8. #17989476 | C22 | semidirect |
| 11. #17989448 | C22 | semidirect |
| 33. D8×D73 | C8 | semidirect |
| 74. D584 | C2×C8 | semidirect |
| 92. D8×C73 | C2×C8 | semidirect |
| 158. D73 | #1333 | semidirect |
| 164. C73 | C2×#1333 | semidirect |
| 235. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626132 | 2 |
| #22625473 | 2 |
| #22624890 | 2 |
| #22624889 | 2 |
| C4×D8×D73 | 2 |
| C2×#1333 | 73 |