Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 80 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×#64408 | C2 | semidirect |
| 3. #22625501 | C2 | semidirect |
| 5. #22624823 | C2 | semidirect |
| 6. #22624758 | C2 | semidirect |
| 23. #17988334 | C4 | semidirect |
| 24. #17988332 | C4 | semidirect |
| 25. #17988331 | C4 | semidirect |
| 26. #331×C73 | C4 | semidirect |
| 180. C73 | #9577 | semidirect |
| 197. #331 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626065 | 2 |
| C4⋊C8×#64408 | 2 |
| #22625501 | 2 |
| #22625237 | 2 |
| #22624823 | 2 |
| #22624758 | 2 |
| #22608577 | 2 |
| #9577 | 73 |