Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
376 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22588386 | C2 | semidirect |
| 3. #22586329 | C2 | semidirect |
| 4. #22586326 | C2 | semidirect |
| 5. C71×#2115 | C2 | semidirect |
| 6. C2×#14556150 | C4 | semidirect |
| 8. #17986257 | C4 | semidirect |
| 10. #17986252 | C4 | semidirect |
| 15. C2×#14556060 | C4 | semidirect |
| 173. #2115 | D71 | semidirect |
| 177. C71 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598002 | 2 |
| #22588386 | 2 |
| #22586329 | 2 |
| #22586326 | 2 |
| C71×#2115 | 2 |
| #11867 | 71 |