Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597193 | C2 | semidirect |
| 3. C2×#17985811 | C2 | semidirect |
| 4. #22590056 | C2 | semidirect |
| 5. #22586437 | C2 | semidirect |
| 6. #22586429 | C2 | semidirect |
| 7. C71×#1978 | C2 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 43. C2×C71⋊C16 | C2×C4 | semidirect |
| 53. C2×D8×C71 | C2×C4 | semidirect |
| 170. #1978 | D71 | semidirect |
| 173. C71 | #13017 | semidirect |
| 205. C2×D8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| #22597193 | 2 |
| C2×#17985811 | 2 |
| #22590056 | 2 |
| #22586437 | 2 |
| #22586429 | 2 |
| C71×#1978 | 2 |
| #13017 | 71 |