Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22590112 | C2 | semidirect |
| 2. C2×#17985812 | C2 | semidirect |
| 3. #22590056 | C2 | semidirect |
| 4. #22589968 | C2 | semidirect |
| 5. #22588394 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 32. C2×C71⋊C16 | D4 | semidirect |
| 173. C71 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590112 | 2 |
| C2×#17985812 | 2 |
| #22590056 | 2 |
| #22589968 | 2 |
| #22588394 | 2 |
| #22586441 | 2 |
| C71×#3058 | 2 |
| #13396 | 71 |