Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22590183 | C2 | semidirect |
| 3. #22586407 | C2 | semidirect |
| 4. #22586316 | C2 | semidirect |
| 5. #22586315 | C2 | semidirect |
| 6. #22586262 | C2 | semidirect |
| 7. C71×#2171 | C2 | semidirect |
| 25. #14556074 | C8 | semidirect |
| 26. #14556072 | C8 | semidirect |
| 27. #14556071 | C8 | semidirect |
| 28. #14556069 | C8 | semidirect |
| 104. #2171 | D71 | semidirect |
| 109. C71 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590224 | 2 |
| #22590183 | 2 |
| #22586407 | 2 |
| #22586316 | 2 |
| #22586315 | 2 |
| #22586262 | 2 |
| C71×#2171 | 2 |
| #12068 | 71 |