Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #22599088 | C2 | semidirect |
| 2. #22597592 | C2 | semidirect |
| 3. #22588252 | C2 | semidirect |
| 4. #22586701 | C2 | semidirect |
| 5. #22586700 | C2 | semidirect |
| 6. #22586216 | C2 | semidirect |
| 7. C71×#3006 | C2 | semidirect |
| 258. #3006 | D71 | semidirect |
| 263. C71 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599088 | 2 |
| #22597592 | 2 |
| #22588252 | 2 |
| #22586701 | 2 |
| #22586700 | 2 |
| #22586216 | 2 |
| C71×#3006 | 2 |
| #9974 | 71 |