Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
972 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 2. #22612549 | C2 | semidirect |
| 4. #22607811 | C2 | semidirect |
| 5. C2×#324×C73 | C2 | semidirect |
| 12. #17988504 | C4 | semidirect |
| 153. C2×C4×C73 | #102 | semidirect |
| 216. C2×#324 | D73 | semidirect |
| 218. C73 | #9019 | semidirect |
| 377. C2×C4 | #14556513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988504 | 2 |
| #22612549 | 2 |
| #22609863 | 2 |
| #22607811 | 2 |
| C2×#324×C73 | 2 |
| #9019 | 73 |