Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 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. #22599327 | C2 | semidirect |
| 2. #22598790 | C2 | semidirect |
| 3. #22587054 | C2 | semidirect |
| 4. #22586938 | C2 | semidirect |
| 5. #22586847 | C2 | semidirect |
| 6. #22586233 | C2 | semidirect |
| 7. C71×#2657 | C2 | semidirect |
| 38. #14556128 | D4 | semidirect |
| 39. #14556125 | D4 | semidirect |
| 46. C4⋊(C71⋊C8) | D4 | semidirect |
| 53. #14556039 | D4 | semidirect |
| 214. #2657 | D71 | semidirect |
| 219. C71 | #10088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599327 | 2 |
| #22598790 | 2 |
| #22587054 | 2 |
| #22586938 | 2 |
| #22586847 | 2 |
| #22586233 | 2 |
| C71×#2657 | 2 |
| #10088 | 71 |