Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22590140 | C2 | semidirect |
| 3. #22590136 | C2 | semidirect |
| 4. #22586264 | C2 | semidirect |
| 5. #22586263 | C2 | semidirect |
| 6. #22586263 | C2 | semidirect |
| 7. C71×#1314 | C2 | semidirect |
| 186. #1314 | D71 | semidirect |
| 187. C71 | #11489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986074 | 2 |
| #22590140 | 2 |
| #22590136 | 2 |
| #22586264 | 2 |
| #22586263 | 2 |
| C71×#1314 | 2 |
| #11489 | 71 |