Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 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. #22598462 | C2 | semidirect |
| 3. #22586975 | C2 | semidirect |
| 4. #22586810 | C2 | semidirect |
| 5. #22586684 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#3103 | C2 | semidirect |
| 199. #3103 | D71 | semidirect |
| 204. C71 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599331 | 2 |
| #22598462 | 2 |
| #22586975 | 2 |
| #22586810 | 2 |
| #22586684 | 2 |
| #22586202 | 2 |
| C71×#3103 | 2 |
| #10040 | 71 |