Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22590015 | C2 | semidirect |
| 5. #22588626 | C2 | semidirect |
| 6. #22586470 | C2 | semidirect |
| 7. C71×#1915 | C2 | semidirect |
| 198. #1915 | D71 | semidirect |
| 202. C71 | #13433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599207 | 2 |
| #22590015 | 2 |
| #22589991 | 2 |
| #22588867 | 2 |
| #22588626 | 2 |
| #22586470 | 2 |
| C71×#1915 | 2 |
| #13433 | 71 |