Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 2. #22590095 | C2 | semidirect |
| 5. #22588501 | C2 | semidirect |
| 6. #22586445 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 11. #17986093 | C4 | semidirect |
| 13. #17986081 | C4 | semidirect |
| 164. #1386 | D71 | semidirect |
| 165. C71 | #12817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597111 | 2 |
| #22590095 | 2 |
| C2×#17985810 | 2 |
| C2×#17985808 | 2 |
| #22588501 | 2 |
| #22586445 | 2 |
| C71×#1386 | 2 |
| #12817 | 71 |