Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22599556 | C2 | semidirect |
| 4. #22589320 | C2 | semidirect |
| 5. #22586853 | C2 | semidirect |
| 7. C71×#1307 | C2 | semidirect |
| 198. #1307 | D71 | semidirect |
| 199. C71 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599728 | 2 |
| #22599556 | 2 |
| #22599353 | 2 |
| #22589320 | 2 |
| #22586853 | 2 |
| #22586849 | 2 |
| C71×#1307 | 2 |
| #10215 | 71 |