Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22607877 | C2 | semidirect |
| 3. #22607865 | C2 | semidirect |
| 47. C2×Q8×C73 | M16 | semidirect |
| 74. C42×C73 | M16 | semidirect |
| 139. C73 | #11535 | semidirect |
| 180. C2×Q8 | #11924012 | semidirect |
| 209. C42 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608269 | 2 |
| #22607877 | 2 |
| #22607865 | 2 |
| C73×#2326 | 2 |
| #11535 | 73 |