Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22586934 | C2 | semidirect |
| 4. #22586762 | C2 | semidirect |
| 6. #22586629 | C2 | semidirect |
| 7. C4×#108×C71 | C2 | semidirect |
| 177. C4×#108 | D71 | semidirect |
| 183. C71 | #9728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598899 | 2 |
| #22586934 | 2 |
| #22586931 | 2 |
| #22586762 | 2 |
| #22586758 | 2 |
| #22586629 | 2 |
| C4×#108×C71 | 2 |
| #9728 | 71 |