Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 122 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. #22624752 | C2 | semidirect |
| 4. #22624749 | C2 | semidirect |
| 35. #14556571 | C8 | semidirect |
| 68. C2×Dic146 | C2×C8 | semidirect |
| 104. C4⋊C4×C73 | C2×C8 | semidirect |
| 199. C73 | #7589 | semidirect |
| 292. C4⋊C4 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625788 | 2 |
| #22625592 | 2 |
| #22624752 | 2 |
| #22624749 | 2 |
| C4×#14556571 | 2 |
| #7589 | 73 |