Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
602 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #22586654 | C2 | semidirect |
| 2. #22586274 | C2 | semidirect |
| 3. #22586272 | C2 | semidirect |
| 24. C2×#41×C71 | C8 | semidirect |
| 173. C71 | #11431 | semidirect |
| 190. C2×#41 | C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586654 | 2 |
| #22586274 | 2 |
| #22586272 | 2 |
| C71×#2297 | 2 |
| #11431 | 71 |