Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 109 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. C4⋊C8×Dic73 | C2 | semidirect |
| 3. #22608702 | C2 | semidirect |
| 5. #22607828 | C2 | semidirect |
| 6. #22607763 | C2 | semidirect |
| 21. #332×C73 | C4 | semidirect |
| 22. #331×C73 | C4 | semidirect |
| 163. C73 | #9578 | semidirect |
| 176. #332 | Dic73 | semidirect |
| 177. #331 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610760 | 2 |
| C4⋊C8×Dic73 | 2 |
| #22608702 | 2 |
| #22608330 | 2 |
| #22607828 | 2 |
| #22607763 | 2 |
| C73×#1540 | 2 |
| #9578 | 73 |