Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22599488 | C2 | semidirect |
| 4. #22589263 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1986 | C2 | semidirect |
| 193. #1986 | D71 | semidirect |
| 197. C71 | #10202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599652 | 2 |
| #22599488 | 2 |
| #22598734 | 2 |
| #22589263 | 2 |
| #22586834 | 2 |
| #22586191 | 2 |
| C71×#1986 | 2 |
| #10202 | 71 |