Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 41. #14556068 | Q8 | semidirect |
| 59. M32×C71 | Q8 | semidirect |
| 65. #106×C71 | Q8 | semidirect |
| 163. C71 | #13454 | semidirect |
| 202. M32 | Dic142 | semidirect |
| 218. #106 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598863 | 2 |
| #22590129 | 2 |
| #22590128 | 2 |
| #22589084 | 2 |
| #22586447 | 2 |
| #22586423 | 2 |
| C71×#1386 | 2 |
| #13454 | 71 |