Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22590067 | C2 | semidirect |
| 3. #22590055 | C2 | semidirect |
| 4. #22589944 | C2 | semidirect |
| 5. #22589248 | C2 | semidirect |
| 6. #22589236 | C2 | semidirect |
| 7. C71×#2155 | C2 | semidirect |
| 12. C2×#14556073 | C4 | semidirect |
| 13. C2×D1136 | C4 | semidirect |
| 169. #2155 | D71 | semidirect |
| 175. C71 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| #22590067 | 2 |
| #22590055 | 2 |
| #22589944 | 2 |
| #22589248 | 2 |
| #22589236 | 2 |
| C71×#2155 | 2 |
| #13247 | 71 |