Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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. #22598271 | C2 | semidirect |
| 3. #22589557 | C2 | semidirect |
| 4. #22588788 | C2 | semidirect |
| 5. #22588554 | C2 | semidirect |
| 6. #22588298 | C2 | semidirect |
| 7. #22588264 | C2 | semidirect |
| 8. C71×#2310 | C2 | semidirect |
| 207. #2310 | D71 | semidirect |
| 213. C71 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601991 | 2 |
| #22598271 | 2 |
| #22589557 | 2 |
| #22588788 | 2 |
| #22588554 | 2 |
| #22588298 | 2 |
| #22588264 | 2 |
| C71×#2310 | 2 |
| #24023 | 71 |