Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 35. #14556537 | C8 | semidirect |
| 107. C73 | #12044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625519 | 2 |
| Q16×#10596833 | 2 |
| #22624965 | 2 |
| #22624888 | 2 |
| #22624887 | 2 |
| #22624842 | 2 |
| #22611787 | 2 |
| #12044 | 73 |