Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
662 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 662 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. #22596975 | C2 | semidirect |
| 3. #22589916 | C2 | semidirect |
| 4. #22589856 | C2 | semidirect |
| 5. #22589624 | C2 | semidirect |
| 6. #22589012 | C2 | semidirect |
| 7. #22588789 | C2 | semidirect |
| 8. #22588759 | C2 | semidirect |
| 9. #22588578 | C2 | semidirect |
| 10. #22588487 | C2 | semidirect |
| 65. #14556038 | D4 | semidirect |
| 67. C8×Dic71 | D4 | semidirect |
| 206. C71 | #29385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597250 | 2 |
| #22596975 | 2 |
| #22589916 | 2 |
| #22589856 | 2 |
| #22589624 | 2 |
| #22589012 | 2 |
| #22588789 | 2 |
| #22588759 | 2 |
| #22588578 | 2 |
| #22588487 | 2 |
| C71×#2010 | 2 |
| #29385 | 71 |