Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 116 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. #22626263 | C2 | semidirect |
| 2. C4×#14556665 | C2 | semidirect |
| 3. #22624884 | C2 | semidirect |
| 8. C4⋊#11924031 | C22 | semidirect |
| 9. #17989475 | C22 | semidirect |
| 136. C73 | #11587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C4×#14556665 | 2 |
| #22624884 | 2 |
| C2×#17988664 | 2 |
| #11587 | 73 |