Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 3. #22590059 | C2 | semidirect |
| 4. #22589944 | C2 | semidirect |
| 5. #22589253 | C2 | semidirect |
| 7. C71×#2155 | C2 | semidirect |
| 12. C2×Dic568 | C4 | semidirect |
| 13. C2×#14556073 | C4 | semidirect |
| 164. #2155 | D71 | semidirect |
| 170. C71 | #13248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986442 | 2 |
| #22590067 | 2 |
| #22590059 | 2 |
| #22589944 | 2 |
| #22589253 | 2 |
| #22589236 | 2 |
| C71×#2155 | 2 |
| #13248 | 71 |