Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1318 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 235 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. #22596783 | C2 | semidirect |
| 3. #22588807 | C2 | semidirect |
| 4. #22588802 | C2 | semidirect |
| 5. #22588420 | C2 | semidirect |
| 6. #22588266 | C2 | semidirect |
| 7. C71×#1821 | C2 | semidirect |
| 190. #1821 | D71 | semidirect |
| 192. C71 | #21757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986580 | 2 |
| #22596783 | 2 |
| #22588807 | 2 |
| #22588802 | 2 |
| #22588420 | 2 |
| #22588266 | 2 |
| C71×#1821 | 2 |
| #21757 | 71 |