Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22590087 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22589950 | C2 | semidirect |
| 5. #22588375 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#2155 | C2 | semidirect |
| 62. C2×C16×C71 | D4 | semidirect |
| 183. #2155 | D71 | semidirect |
| 189. C71 | #13395 | semidirect |
| 239. C2×C16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597922 | 2 |
| #22590087 | 2 |
| #22590069 | 2 |
| #22589950 | 2 |
| #22588375 | 2 |
| #22586456 | 2 |
| C71×#2155 | 2 |
| #13395 | 71 |