Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22588095 | C2 | semidirect |
| 3. #22586335 | C2 | semidirect |
| 5. #22586329 | C2 | semidirect |
| 7. C71×#2166 | C2 | semidirect |
| 9. #17986397 | C4 | semidirect |
| 10. #17986383 | C4 | semidirect |
| 15. #17986112 | C4 | semidirect |
| 16. #17986107 | C4 | semidirect |
| 146. #2166 | D71 | semidirect |
| 152. C71 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598957 | 2 |
| #22588095 | 2 |
| #22586335 | 2 |
| #22586332 | 2 |
| #22586329 | 2 |
| #22586326 | 2 |
| C71×#2166 | 2 |
| #11769 | 71 |