Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22586905 | C2 | semidirect |
| 4. #22586838 | C2 | semidirect |
| 6. #22586200 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 12. #17986290 | C4 | semidirect |
| 13. #17986280 | C4 | semidirect |
| 32. #14556128 | C2×C4 | semidirect |
| 33. #14556128 | C2×C4 | semidirect |
| 67. C4⋊C8×C71 | C2×C4 | semidirect |
| 201. #1303 | D71 | semidirect |
| 203. C71 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598139 | 2 |
| #22591251 | 2 |
| #22586905 | 2 |
| #22586838 | 2 |
| #22586732 | 2 |
| #22586200 | 2 |
| C71×#1303 | 2 |
| #9175 | 71 |