Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22624873 | C2 | semidirect |
| 3. #22624861 | C2 | semidirect |
| 38. #124×C73 | C8 | semidirect |
| 64. C2×Q8×C73 | C2×C8 | semidirect |
| 74. C42×C73 | C2×C8 | semidirect |
| 139. C73 | #11481 | semidirect |
| 157. #124 | #10596833 | semidirect |
| 180. C2×Q8 | C2×#10596833 | semidirect |
| 209. C42 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625167 | 2 |
| #22624873 | 2 |
| #22624861 | 2 |
| #22612644 | 2 |
| #11481 | 73 |