Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
654 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. #22597250 | C2 | semidirect |
| 2. #22596983 | C2 | semidirect |
| 3. #22589920 | C2 | semidirect |
| 4. #22589894 | C2 | semidirect |
| 6. #22589046 | C2 | semidirect |
| 7. #22588838 | C2 | semidirect |
| 8. #22588700 | C2 | semidirect |
| 9. #22588628 | C2 | semidirect |
| 10. #22588487 | C2 | semidirect |
| 11. C71×#2053 | C2 | semidirect |
| 195. #2053 | D71 | semidirect |
| 202. C71 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597250 | 2 |
| #22596983 | 2 |
| #22589920 | 2 |
| #22589894 | 2 |
| #22589443 | 2 |
| #22589046 | 2 |
| #22588838 | 2 |
| #22588700 | 2 |
| #22588628 | 2 |
| #22588487 | 2 |
| C71×#2053 | 2 |
| #29386 | 71 |