Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22588329 | C2 | semidirect |
| 3. #22587018 | C2 | semidirect |
| 4. #22586792 | C2 | semidirect |
| 5. C2×#17985728 | C2 | semidirect |
| 6. #22586214 | C2 | semidirect |
| 7. C71×#1567 | C2 | semidirect |
| 203. #1567 | D71 | semidirect |
| 208. C71 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597806 | 2 |
| #22588329 | 2 |
| #22587018 | 2 |
| #22586792 | 2 |
| C2×#17985728 | 2 |
| #22586214 | 2 |
| C71×#1567 | 2 |
| #10456 | 71 |