Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 4. #22586891 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586204 | C2 | semidirect |
| 7. C71×#1515 | C2 | semidirect |
| 10. #17986347 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 43. C4×C71⋊C8 | C2×C4 | semidirect |
| 47. C4⋊Q8×C71 | C2×C4 | semidirect |
| 48. C4⋊Q8×C71 | C2×C4 | semidirect |
| 172. #1515 | D71 | semidirect |
| 175. C71 | #9425 | semidirect |
| 198. C4⋊Q8 | C4×D71 | semidirect |
| 199. C4⋊Q8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598716 | 2 |
| #22591516 | 2 |
| #22587053 | 2 |
| #22586891 | 2 |
| #22586206 | 2 |
| #22586204 | 2 |
| C71×#1515 | 2 |
| #9425 | 71 |