Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. #22625132 | C2 | semidirect |
| 4. #22624775 | C2 | semidirect |
| 36. #14556651 | C8 | semidirect |
| 57. #11924037 | C2×C8 | semidirect |
| 133. #10596833 | #100 | semidirect |
| 171. C73 | C8×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989614 | 2 |
| #22625681 | 2 |
| #22625132 | 2 |
| #22624775 | 2 |
| #22608250 | 2 |
| C8×#100 | 73 |