Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 105. C2×Q8×C71 | Q16 | semidirect |
| 188. C71 | #10183 | semidirect |
| 266. C2×Q8 | Dic284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599290 | 2 |
| #22598145 | 2 |
| C2×#17986294 | 2 |
| #22587024 | 2 |
| #22586744 | 2 |
| #22586236 | 2 |
| C71×#1461 | 2 |
| #10183 | 71 |