Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 97. C2×C8×C71 | Q16 | semidirect |
| 177. C71 | #10224 | semidirect |
| 262. C2×C8 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599488 | 2 |
| #22599285 | 2 |
| #22589313 | 2 |
| #22586904 | 2 |
| #22586185 | 2 |
| C71×#3162 | 2 |
| #10224 | 71 |