Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22625233 | C2 | semidirect |
| 4. #22624755 | C2 | semidirect |
| 49. #124×C73 | C8 | semidirect |
| 78. C2×Q8×C73 | C2×C8 | semidirect |
| 88. C42×C73 | C2×C8 | semidirect |
| 157. C73 | #9099 | semidirect |
| 178. #124 | #10596833 | semidirect |
| 208. C2×Q8 | C2×#10596833 | semidirect |
| 240. C42 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626778 | 2 |
| #22625233 | 2 |
| #22625171 | 2 |
| #22624755 | 2 |
| #22612644 | 2 |
| #9099 | 73 |