Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22590113 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22590057 | C2 | semidirect |
| 5. #22589250 | C2 | semidirect |
| 6. #22589238 | C2 | semidirect |
| 7. C71×#2110 | C2 | semidirect |
| 12. C2×#14556073 | C4 | semidirect |
| 13. C2×D1136 | C4 | semidirect |
| 172. #2110 | 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 |
| #22590113 | 2 |
| #22590069 | 2 |
| #22590057 | 2 |
| #22589250 | 2 |
| #22589238 | 2 |
| C71×#2110 | 2 |
| #13247 | 71 |