Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588386 | C2 | semidirect |
| 4. #22586460 | C2 | semidirect |
| 5. C71×#1812 | C2 | semidirect |
| 6. C2×#14556134 | C4 | semidirect |
| 13. #17986022 | C4 | semidirect |
| 15. #17985967 | C4 | semidirect |
| 17. C2×C8×Dic71 | C4 | semidirect |
| 189. #1812 | D71 | semidirect |
| 191. C71 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597050 | 2 |
| #22590003 | 2 |
| #22588386 | 2 |
| #22586460 | 2 |
| C71×#1812 | 2 |
| #12807 | 71 |