Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22589316 | C2 | semidirect |
| 4. C4×#14556038 | C2 | semidirect |
| 5. #22586794 | C2 | semidirect |
| 7. C71×#1567 | C2 | semidirect |
| 10. #17986397 | C4 | semidirect |
| 11. #17986372 | C4 | semidirect |
| 12. #17986350 | C4 | semidirect |
| 13. #17986346 | C4 | semidirect |
| 140. C8×C71 | #104 | semidirect |
| 170. #1567 | D71 | semidirect |
| 173. C71 | #9851 | semidirect |
| 307. C8 | #14556054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598899 | 2 |
| #22589316 | 2 |
| #22589167 | 2 |
| C4×#14556038 | 2 |
| #22586794 | 2 |
| #22586790 | 2 |
| C71×#1567 | 2 |
| #9851 | 71 |