Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
618 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22627073 | C2 | semidirect |
| 2. C42×#10596842 | C2 | semidirect |
| 3. C2×Q8⋊#10596842 | C2 | semidirect |
| 47. #14556580 | C8 | semidirect |
| 48. #14556579 | C8 | semidirect |
| 49. #14556578 | C8 | semidirect |
| 53. #124×C73 | C8 | semidirect |
| 177. C73 | #9639 | semidirect |
| 202. #124 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| C42×#10596842 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C2×D4⋊#10596842 | 2 |
| #124×#64408 | 2 |
| #9639 | 73 |