Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 152 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. #22624848 | C2 | semidirect |
| 4. #22624847 | C2 | semidirect |
| 26. C2×#11924003 | C8 | semidirect |
| 34. C2×C16×C73 | C8 | semidirect |
| 86. C73 | #11405 | semidirect |
| 108. C2×C16 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626137 | 2 |
| #22625134 | 2 |
| #22624848 | 2 |
| #22624847 | 2 |
| C2×#17988362 | 2 |
| #11405 | 73 |