Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22588336 | C2 | semidirect |
| 4. #22586466 | C2 | semidirect |
| 5. C71×#1801 | C2 | semidirect |
| 188. C4×C71 | #355 | semidirect |
| 202. #1801 | D71 | semidirect |
| 204. C71 | #12801 | semidirect |
| 390. C4 | #17985795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556117 | 2 |
| C2×#17985795 | 2 |
| #22588336 | 2 |
| #22586466 | 2 |
| C71×#1801 | 2 |
| #12801 | 71 |