Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 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. #22597280 | C2 | semidirect |
| 3. #22586998 | C2 | semidirect |
| 5. #22586237 | C2 | semidirect |
| 6. #22586185 | C2 | semidirect |
| 109. C2×C8×C71 | SD16 | semidirect |
| 196. C71 | #9050 | semidirect |
| 290. C2×C8 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598348 | 2 |
| #22597280 | 2 |
| #22586998 | 2 |
| #22586765 | 2 |
| #22586237 | 2 |
| #22586185 | 2 |
| C71×#1955 | 2 |
| #9050 | 71 |