Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22599723 | C2 | semidirect |
| 3. #22587480 | C2 | semidirect |
| 4. #22587461 | C2 | semidirect |
| 5. #22587418 | C2 | semidirect |
| 6. #22587399 | C2 | semidirect |
| 7. #22587075 | C2 | semidirect |
| 8. #22586795 | C2 | semidirect |
| 9. C71×#3550 | C2 | semidirect |
| 191. #3550 | D71 | semidirect |
| 200. C71 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599723 | 2 |
| #22598766 | 2 |
| #22587480 | 2 |
| #22587461 | 2 |
| #22587418 | 2 |
| #22587399 | 2 |
| #22587075 | 2 |
| #22586795 | 2 |
| C71×#3550 | 2 |
| #18688 | 71 |