Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 107. C2×C8×C71 | Q16 | semidirect |
| 174. C71 | #9048 | semidirect |
| 260. C2×C8 | Dic284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598380 | 2 |
| #22597280 | 2 |
| #22589280 | 2 |
| #22586995 | 2 |
| #22586770 | 2 |
| #22586236 | 2 |
| C71×#1281 | 2 |
| #9048 | 71 |