Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22590113 | C2 | semidirect |
| 2. #22590068 | C2 | semidirect |
| 3. #22590056 | C2 | semidirect |
| 4. #22589944 | C2 | semidirect |
| 5. #22589251 | C2 | semidirect |
| 6. #22589239 | C2 | semidirect |
| 24. C2×SD32×C71 | C4 | semidirect |
| 25. C2×D16×C71 | C4 | semidirect |
| 175. C71 | #13247 | semidirect |
| 180. C2×SD32 | Dic71 | semidirect |
| 181. C2×D16 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590113 | 2 |
| #22590068 | 2 |
| #22590056 | 2 |
| #22589944 | 2 |
| #22589251 | 2 |
| #22589239 | 2 |
| C2×#509×C71 | 2 |
| #13247 | 71 |