Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 23. #17988335 | C4 | semidirect |
| 24. #17988335 | C4 | semidirect |
| 25. #17988333 | C4 | semidirect |
| 26. #332×C73 | C4 | semidirect |
| 163. C73 | #9580 | semidirect |
| 180. #332 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626116 | 2 |
| C4⋊C8×#64408 | 2 |
| #22625501 | 2 |
| #22625240 | 2 |
| #22624823 | 2 |
| #22624758 | 2 |
| #22608587 | 2 |
| #9580 | 73 |