Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 44. M16×C73 | C16 | semidirect |
| 88. C73 | #7163 | semidirect |
| 120. M16 | #11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626288 | 2 |
| C2×C4×#11924031 | 2 |
| M16×#10596831 | 2 |
| #7163 | 73 |