Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
272 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 71. Q16×C71 | Q16 | semidirect |
| 137. C71 | #12415 | semidirect |
| 196. Q16 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590627 | 2 |
| #22590492 | 2 |
| #22587858 | 2 |
| #22586392 | 2 |
| #22586322 | 2 |
| #22586310 | 2 |
| C71×#3390 | 2 |
| #12415 | 71 |