Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597059 | C2 | semidirect |
| 3. #22586990 | C2 | semidirect |
| 4. #22586765 | C2 | semidirect |
| 5. #22586237 | C2 | semidirect |
| 6. #22586185 | C2 | semidirect |
| 7. C71×#1955 | C2 | semidirect |
| 117. C2×C8×C71 | D8 | semidirect |
| 210. #1955 | D71 | semidirect |
| 215. C71 | #9049 | semidirect |
| 321. C2×C8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598340 | 2 |
| #22597059 | 2 |
| #22586990 | 2 |
| #22586765 | 2 |
| #22586237 | 2 |
| #22586185 | 2 |
| C71×#1955 | 2 |
| #9049 | 71 |