Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
252 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 5. #17989455 | C4 | semidirect |
| 7. C2×#14556531 | C4 | semidirect |
| 9. C22×C16×C73 | C4 | semidirect |
| 81. C73 | #7228 | semidirect |
| 84. C22×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625813 | 2 |
| #22611544 | 2 |
| #7228 | 73 |