Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 34. C2×C8×C73 | C16 | semidirect |
| 74. C73 | #7145 | semidirect |
| 105. C2×C8 | #11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626288 | 2 |
| C2×#17988308 | 2 |
| #7145 | 73 |