Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
218 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11765855 | C16 | direct (N × H) |
| 64. C16×C71 | Q16 | semidirect |
| 105. C71 | C16×Q16 | semidirect |
| 162. C16 | #11765855 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic142 | 2 |
| C8×#11765855 | 2 |
| #22586409 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586318 | 2 |
| C16×C71⋊C8 | 2 |
| Q8×C16×C71 | 2 |
| C16×Q16 | 71 |